In
2017, as a freshman at Kentucky, Thompson appeared in twenty games (13 starts) in which he went 8–3 with a 3.45 ERA.[4] As a sophomore in
2018, Thompson missed nearly two months due to an elbow injury.[5][6] He appeared in nine games, making seven starts, going 2–1 with a 4.94 ERA.[7][8] That summer, Thompson played in the
Cape Cod Baseball League for the
Brewster Whitecaps and also played for the
USA Baseball Collegiate National Team.[9][10][11][12][13] Prior to the
2019 season, Thompson was named to the Preseason All-SEC First Team.[14] He was named the SEC Pitcher of the Week on April 1 after throwing a complete-game shutout against the
Georgia Bulldogs in which he struck out 13 batters while allowing only two hits.[15] Thompson finished his junior year with a 6-1 record and a 2.40 ERA over 14 starts, striking out 130 batters in ninety innings, earning a spot on the All-SEC Second Team.[16]
Thompson did not play a minor league game in 2020 due to the cancellation of the minor league season caused by the
COVID-19 pandemic.[24] Before the 2021 minor league season began, he participated in spring training with the major league club.[25] Afterwards, Thompson was assigned to the
Memphis Redbirds of the
Triple-A East, appearing in 22 games (19 starts) in which he went 2-10 with a 7.06 ERA, 82 strikeouts, and 57 walks over 93 innings.[26] Thompson was selected to play in the
Arizona Fall League (AFL) for the
Glendale Desert Dogs after the season where he was named to the Fall Stars Game.[27][28] Over 17+1⁄3 innings pitched during the AFL, Thompson went 3-0 with a 1.56 ERA, 22 strikeouts, and 15 walks.[29]
Thompson returned to Memphis to begin the 2022 season.[30] After starting ten games and going 2-2 with a 4.67 ERA, the Cardinals selected his contract and promoted him to the major leagues on June 3.[31] Thompson became the first Cardinals player to wear uniform number 57 since the death of
Darryl Kile during the 2002 season.[32] He made his MLB debut that day at
Wrigley Field versus the
Chicago Cubs, throwing four innings in relief, giving up one run, three hits, and one walk while striking out three batters and recording a
save.[33]