2018–20

On 18 January 2018, it was announced that a deal had been agreed with SønderjyskE for Uhre to join Brøndby IF on 15 June 2018 on a four-and-a-half year deal.^[4][14] The transfer fee was later revealed to be around 3 million DKK.^[15] On 16 July, Uhre made his debut for Brøndby in a Superliga match against Randers FC. The match ended in a 2–0 away win for Brøndby.^[16]

On 29 July, Uhre came off the bench against Hobro IK substituting Ante Erceg in the 68th minute. Subsequently, he secured a 2–1 away win for Brøndby, scoring the winning goal deep in injury time.^[17] He finished the 2018–19 season with 6 goals in 28 league matches. During large parts of the 2018–19 season, Uhre was mostly used as a substitute for regular strikers Kamil Wilczek and Simon Hedlund.

On 21 June 2020, he scored the decisive 1–1 equaliser off a bad return ball to seal a draw against FC Copenhagen in the 89th minute.^[18][19] This marked his first goal in 11 months, and came after him coming on as a substitute for Sigurd Rosted in the 84th minute.^[20] He would then feature as a starter in Brøndby's following matches, after Hedlund and Mráz had been tested positive for COVID-19.^[8] On 9 July, Uhre provided an assist and netted a hat-trick in the club's 4–0 victory over FC Nordsjælland.^[21][22] Thereafter, he became an established starter for Brøndby.

2020–21: Top goalscorer

In the second match-day of the 2020–21 season, on 20 September 2020, Uhre scored the winner deep into stoppage time in a derby against Copenhagen as Brøndby won 2–1.^[23] He had also earlier provided an assist to Jesper Lindstrøm who had netted the equaliser after former Brøndby player Kamil Wilczek had scored the opener for Copenhagen.^[23][24] His strong form continued throughout the fall, and he topped the list of players in the Superliga with most goals and assists combined in late November.^[25] He was voted Player of the Month in December 2020 by Brøndby's fans, having scored three goals in four appearances during the month.^[26]

On 14 March 2021, Uhre scored a perfect hat-trick in the first half of the Superliga match against Odense Boldklub – all from assists from Jesper Lindstrøm – sealing the 0–3 win for Brøndby and the first place in the league table ahead of the championship round.^[27][28] His performances led to him being named Superliga Player of the Month for March.^[29] As Brøndby qualified for the championship round, Uhre's goalscoring continued with goals against Copenhagen, Nordsjælland, Randers, Midtjylland and a brace against AGF on 20 May, which propelled the club to a first place in the league table with one match to go.^[30][31] Earlier that day, he was voted the Tipsbladet Player of the Spring by managers of the Superliga.^[32] On 24 May, as Brøndby won their first league title in 16 years after a 2–0 win over Nordsjælland, Uhre became top goalscorer of the Superliga with 19 goals to his name.^[33]

At the end of the season, Uhre was awarded with the Danish Superliga Player of the Season award.^[34]

2021–22

Uhre scored his first goal of the 2021–22 season on the third matchday against Vejle Boldklub.^[35] On 17 August 2021, Uhre scored the opener in a 1–2 loss to Red Bull Salzburg in the first leg of the play-off round of the UEFA Champions League.^[36] He also scored a brace against OB and a goal against Midtjylland to bring his season total to five goals in nine games.^[37][38]