2016

Vesti started his career in Danish Formula Ford, in which he managed to finish fourth in the championship.^[5]

2017

In 2017, Vesti competed in the German and Danish Formula 4 Championships. Despite missing two events of the Danish Championship, the Danish driver managed to finish second in his debut F4 season, finishing all races on the podium and helping his team, Vesti Motorsport, to win the team championship.^[6][7] In the German championship, Vesti took his first podium by taking second in the second round at Lausitzring.^[8] Two rounds later, he would claim his first and only win of the season.^[9] Vesti took another podium en route to finishing seventh in the standings.^[10] Vesti also made a one-off appearance in the Formula 4 United States Championship during the final round.^[11]

2018

In 2018, Vesti would yet again compete in the German F4 Championship with Van Amersfoort Racing.^[12] After starting the season with two podiums in the opening two rounds, he claimed his maiden win during the second Hockenheimring round.^[13] His second win came during the next round at the Nürburgring.^[14] Vesti eventually ended fourth in the standings, collecting six other podiums along with his two wins.^[15] The Danish driver also participated in one round at Circuit Paul Ricard during the Italian F4 Championship with VAR. Vesti claimed two wins in the three races, which placed him tenth in the championship.^[16][17][18] Vesti also participated in the final round of the European Formula 3 Championship.^[19][20] He made his debut in the Macau Grand Prix, where he finished 15th.^[21][22]

2020

Vesti tested for Prema Racing during the 2019 post-season test.^[30] At the start of January 2020, Vesti was announced to continue driving for Prema, progressing to the FIA Formula 3 Championship, partnering with Formula Renault Eurocup champion Oscar Piastri and American driver Logan Sargeant.^[31][32] Vesti's first weekend at the Red Bull Ring was decent, scoring a fourth and sixth place.^[33] During the second Red Bull Ring round, he stormed to his first pole position in the championship.^[34][35] He controlled the race and won perfectly, despite it being cut short due to treacherous weather conditions.^[36][37] The next day, he finished in eighth place.^[38] Vesti had a torrid Budapest round; he was caught up in a collision during Race 1 after qualifying fourth.^[39] In Race 2, he worked his way up to 19th before damaging his suspension in a collision with Jack Doohan, putting Vesti into retirement.^[40]

In the first Silverstone round, Vesti had a quiet weekend, scoring two fifth places.^[41] He scored fourth in qualifying for the second Silverstone round, and finished the races in fourth and eighth.^[42] Vesti had another weekend to forget in Barcelona, qualifying poorly in 15th. He barely progressed up the field in Race 1 before retiring with a mechanical issue on lap 9.^[43] He could only improve to 21st place in Race 2.^[44]

In Spa-Francorchamps, Vesti ended sixth in Race 1. However, starting fifth in Race 2, Vesti worked his way to second place, taking his first podium since the second round.^[45][46] Vesti qualified sixth in Monza but was demoted to start ninth for impeding Jake Hughes in qualifying.^[47] He made a brilliant charge in Race 1, overtaking Théo Pourchaire on the third last lap and claiming his second win overall whilst helping Prema become the teams' champions.^[48][49] In Race 2, he had a race to forget. Despite climbing to third by lap 9, his effort would be undone as he touched teammate Sargeant, damaging Vesti's front wing and taking both out of the race.^[50] In Mugello during Race 1, he remained in third for the first 15 laps but passed Lirim Zendeli and Hughes within the next three. He battled with Hughes in the dying laps but managed to defend and secure his third win.^[51][52] In Race 2, Vesti ended in ninth place.^[53][54] His strong end to the season meant Vesti leaped to fourth in the standings with 146.5 points, 17.5 behind champion Piastri.^[55]

2021

Vesti would sign for ART Grand Prix to race in Formula 3 alongside Russian Aleksandr Smolyar and American Juan Manuel Correa.^[56] After qualifying fifth during the first round in Barcelona, he started the season with seventh in Race 1. Vesti took his first podium of the season with a third place, gaining two places on the penultimate lap after Dennis Hauger and Matteo Nannini collided.^[57] In Race 3, Vesti had a slow start to the race, but recovered to finish seventh.^[58] In Paul Ricard, Vesti claimed his second pole overall.^[59] He had an underwhelming Race 1 and Race 2, taking only one point from the latter race. Vesti was passed by Hauger at the start of Race 3, and later struggled in the wet, losing positions to finish sixth.^[60] At the Red Bull Ring, Vesti would qualify second.^[61] In Race 1, Vesti stalled at the start but managed to progress to 13th, later being promoted to seventh due to multiple penalties.^[62] Vesti would finish second in the second race, inheriting a position on the penultimate lap when Victor Martins slowed.^[63] However in Race 3, he beat out polesitter Hauger early on and defended for his only win of the year.^[64][65]

In Budapest, he qualified seventh but was penalised three places for Race 1 due to driving unnecessarily slowly.^[66] Race 1 was one to forget, as a hydraulic leak saw him retire entering lap 16. After not scoring points in Race 2, he bounced back with seventh place in the next race.^[67] He had a quiet Spa-Francorchamps round, taking fourth and two sixth places.^[68] In Zandvoort he qualified poorly in 13th place, but improved to ninth in the first race. In Race 2, at which point he was mathematically out of the running for the title, Vesti returned to the podium in third place.^[69] He improved to eighth in the final race.^[70] Vesti qualified fourth in the Russia season finale, and ended P8 in the first race. Vesti finished second in the final race of the season at Sochi after passing Clément Novalak late on.^[71][72] He thus overhauled Victor Martins to repeat his previous year's championship finish of fourth place, claiming one pole and a win each, and four more podiums.^[73]

2022: Rookie season

Vesti got his first taste of Formula 2 machinery when he participated in the post-season test in 2021 with ART Grand Prix alongside former F3 title rival Théo Pourchaire.^[74] On 21 January 2022, ART Grand Prix announced that Vesti would join the team for the 2022 season alongside Pourchaire.^[75] Before the season, Vesti stated that he was "hoping to translate points into podiums" after his consistent F3 season.^[76] Vesti started his season poorly, failing to score points during the first two rounds, compounded by poor qualifying.^[77][78] During the third round in Imola, in the feature race, Vesti started on the soft tyres, which allowed him to pit during an early safety car. With many rivals ahead on the alternate strategy, Vesti was able to claim his first points of the year by finishing sixth, after which he stated that he needed to "work on qualifying".^[79] In Barcelona, he banished his qualifying woes to secure third.^[80] He finished seventh in the sprint race and ended up holding his position during the feature race, thus scoring his maiden podium in the category.^[81][82]

Vesti had a point-less weekend in Monaco, as another poor qualifying was caused by a red flag brought out by a rival.^[83] In Baku, Vesti qualified eighth. Late in the race, he seized on a mistake from Jehan Daruvala during the safety car restart to take the lead in the closing laps and claim his maiden Formula 2 victory.^[84][85] Vesti stalled at the start of the feature race, but due to many rivals being involved in incidents, he stayed clean to secure seventh place.^[86] He qualified second on the front row in Silverstone,^[87] and finished sixth after a tight battle with Felipe Drugovich.^[88] In the feature race, he had a terrible start and dropped four positions on the first lap. Still, he would recover to fifth, despite losing fourth to Drugovich on the last lap.^[89] Vesti scored his first pole position of the season at the Red Bull Ring, vanquishing his previous qualifying struggles.^[90][91] He finished 12th in the sprint race, as a track limit penalty deprived him of points.^[92] Vesti fitted wet tyres on a drying track and the strategy failed to work, which resulted in him falling down to 14th by the end of the race.^[93]

He qualified third in Paul Ricard, his third top 3 qualifying in a row.^[94] In the sprint race, he ended fifth after multiple penalties were applied post-race.^[95] In the feature race, he lost a position to Jack Doohan at the start but regained third place after the Australian spun whilst fighting teammate Pourchaire, adding another podium.^[96][97] In Budapest, Vesti ended the sprint race fifth and made an overtaking masterclass on the alternate strategy during the later part of the race, although an early penalty costed him a podium.^[98] Heading into the summer break, Vesti stood sixth in the standings with 91 points.^[99]

However, his second half of his season would be poor, as he failed to score points in the Spa-Francorchamps and Zandvoort rounds, all due to more poor qualifying.^[100][101] In Monza, Vesti started on reverse pole for the sprint race by qualifying tenth. However, he was beaten by Jüri Vips during the lap 4 safety car restart, and was forced to settle for second place.^[102] In the feature race, a timely pit stop saw Vesti in a net position fourth place following the lap 11 safety car restart. He would gain positions when Marcus Armstrong had to serve a penalty, and Vesti also passed Ayumu Iwasa, earning him another second place as he would run out of time to catch winner Jehan Daruvala.^[103][104] He failed to score points during the Yas Marina finale. Vesti ended up ninth in the championship with 117 points, helping ART to third in the teams' standings whilst scoring one win, one pole, and five podiums.^[105]

2023: Title challenge and runner-up finish

Following the season finale at Yas Marina, it was announced that Vesti would move to Prema for the 2023 season alongside Ferrari junior Oliver Bearman.^[106] Vesti qualified fifth for the Bahrain opening round, but was penalised three places for the sprint due to impeding Arthur Leclerc.^[107][108] A gamble to pit in the sprint race failed to come through, with Vesti ending up 17th.^[109] The feature race would be more disappointing for Vesti, as he retired after colliding into Richard Verschoor, and the former was given a five-place grid penalty for the next race.^[110][111] Looking to bounce back in Jeddah, Vesti qualified in seventh and finished one place higher in the sprint.^[112] In the feature race, Vesti took advantage of the leaders spinning out, eventually leading for his first feature race win.^[113][114]

Vesti had a disappointing qualifying in Melbourne with 13th, but fought back in the sprint race for eighth position. He started on the slower tyres for the feature race, and it paid off during a late safety car, which saw the Dane wind up in fourth.^[115] Vesti had another successful weekend in Baku, qualifying fourth. In the sprint race, he remained out of trouble and even lead after a late safety car, but made a mistake at a corner, dropping to second whilst teammate Bearman won.^[116] In the feature race, an early pit stop saw him drop down, but he clawed his way back to fifth, and a further disqualification ahead from Victor Martins promoted Vesti back to fourth place in the race and second in the standings.^[117][118]

In the streets of Monaco, Vesti took his first pole of the year.^[119][120] Vesti ended the sprint race outside the points, but led in a lights-to-flag victory during the feature race and claimed the championship lead by five points.^[121] Vesti qualified in eighth for Barcelona and from third, stormed past Jak Crawford and Amaury Cordeel to lead the sprint race and ultimately take back-to-back wins from there.^[122][123] During the feature race, Vesti ran on the alternate strategy and made an overtaking charge, but ran out of time to chase fourth place from Ayumu Iwasa.^[124] He extended his lead in the standings to eleven points.^[125]

At the Red Bull Ring, Vesti qualified in second.^[126] Vesti narrowly missed points with ninth on Saturday, but took the lead from polesitter Martins in the feature race. He would hold the net race lead by a commanding distance, but a late safety car dented his hopes, as Verschoor and Iwasa on the alternate strategy pitted for fresher tyres. They would both overcome Vesti, and he was left to finish third.^[127][128] Having extended his lead to 20 points, he qualified in tenth in Silverstone, and drove away to his fourth victory of the year in the sprint race by 13 seconds.^[129][130] In the feature race, he was unlucky by pitting before the safety car. He was then hit from behind by Roy Nissany at the safety car restart, which caused the Dane to crash into Roman Staněk ahead, damaging his suspension and causing him to retire.^[131] Pourchaire closed the gap to him by six points with a third place.

In Hungary, Vesti qualified in third.^[132] During the feature race, Vesti passed Martins for second place at the start and would remain there for the rest of the race, extending his gap to Pourchaire in the standings to 11 points.^[133][134] Vesti qualified P2 at Spa-Francorchamps, forming a Prema 1–2 alongside polesitter and teammate Bearman.^[135] In the sprint race, Vesti moved to fourth early on, but slipped back to sixth by race's end.^[136] However, the feature race was over for him before it even begun, spinning out on the reconnaissance lap and failing to start the race, which paid the price as he lost the standings lead to Pourchaire.^[137]

In Zandvoort, Vesti qualified in third.^[138] After a red-flagged sprint race, Vesti headed into the feature race with high hopes, but spun on a damp track and fell to the back. Things took for the worse as his tyres detached from the car following his pit stop.^[139] In Monza, he qualified eighth. Starting third in the sprint race, he bolted to the lead and never looked back, eventually taking his fifth win of the year.^[140][141] However, the feature race ended disastrously on the first lap after Roman Staněk pushed Vesti onto the grass into a spin, and he was out of the race.^[142] This allowed Pourchaire to extend his lead from 9 to 25 points after finishing in third place and getting the fastest lap point.^[143]

In Yas Marina, Vesti qualified ninth, whilst rival Pourchaire qualified 14th. Starting on the reverse front row for the sprint race, he challenged Enzo Fittipaldi into turn 1 but fell back to fourth after being overtaken by Isack Hadjar and Verschoor. He fought back and passed Hadjar and Verschoor before overtaking Fittipaldi with three laps to go to take his sixth win on the season.^[144][145] With Pourchaire finishing seventh, Vesti closed the gap to 16 points, setting up a last-race decider.^[146] In the feature race, after starting ninth, Vesti went longer than his rivals and pitted with 12 laps to go. He charged back up the order, and despite a late last lap collision with Zane Maloney that saw his car launched into the air and nearly into the barriers, he finished in third place.^[147] Despite scoring the most wins out of all the drivers in 2023 he missed out on the title by eleven points as Pourchaire finished in fifth place but was still praised for his great driving skills throughout the season.

Vesti finished second in the championship, securing 6 wins, 10 podiums, 1 pole position, and 3 fastest laps. He also helped Prema to second place in the teams championship, 31 points behind champions ART Grand Prix.