San Diego Padres

Thompson made his professional debut with the Arizona League Padres, tossing 12 innings of 2.25 ERA ball. In 2017, Thompson played for the Single-A Fort Wayne TinCaps, posting a 2-4 record and 4.67 ERA in seven appearances. He returned to Fort Wayne for the 2018 season, pitching to a 6-8 record and 4.94 ERA with 97 strikeouts in 93 innings of work. In 2019, Thompson played for the High-A Lake Elsinore Storm, only appearing in seven games due to injury, and recorded an 0-5 record and 7.66 ERA.^[4] Thompson did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.^[5] The Padres added him to their 40-man roster after the 2020 season.^[6]

On June 20, 2021, Thompson was promoted to the major leagues for the first time.^[7] He made his MLB debut on June 22, pitching one-third of an inning against the Los Angeles Dodgers, and earning a hold.^[8]

Washington Nationals

On July 30, 2021, Thompson and Jordy Barley were traded to the Washington Nationals in exchange for Daniel Hudson.^[9] He was activated the next day and made his Nationals debut on August 2.^[10] In 27 relief appearances, he posted a 4.15 ERA with 21 strikeouts across 21+2⁄3 innings of work.

On April 10, 2022, Thompson was placed on the injured list due to a biceps injury.^[11] He was transferred to the 60-day IL on May 10 with biceps tendinitis.^[12] He was activated on July 1.^[13] On September 5, he earned his first major league save by pitching the final three scoreless innings against the St. Louis Cardinals in a 6-0 Nationals win in St. Louis. In 24 games, Thompson recorded a 2.92 ERA with 15 strikeouts and one save. In 2023, Thompson made 51 relief appearances for Washington, registering a 5.50 ERA with 44 strikeouts across 54.0 innings of work.^[14]

On February 28, 2024, it was announced that Thompson would require Tommy John surgery, ending his season prematurely.^[15]