[3][4] Kowar committed to play college baseball for Clemson University as a high school sophomore but was granted his release following a coaching change.

[9] During the 2017 College World Series, Kowar earned the save in the championship game, pitching 1+2⁄3 scoreless innings in his only relief appearance on the season, clinching Florida's 2017 national title.

[12] Kowar was selected by the Kansas City Royals with the 33rd overall pick in the 2018 Major League Baseball draft, and he signed for $2.1 million.

[17] After pitching to a 5–3 record with a 3.53 ERA in 13 starts, he was promoted to the Northwest Arkansas Naturals of the Double-A Texas League in June,[18] where he finished the season.

[25] In his debut, Kowar gave up four earned runs, allowed three hits, walked two batters, and threw three wild pitches before he was removed from the game in the first inning, getting only two outs.

[26] In 9 appearances (8 starts) during his rookie campaign, Kowar posted a ghastly 0–6 record and 11.27 ERA with 29 strikeouts in 30+1⁄3 innings pitched.

[31] On December 3, he was traded with Cole Phillips by Atlanta to the Seattle Mariners for Jarred Kelenic, Marco Gonzales, and Evan White.

[32] On March 10, 2024, the Mariners announced Kowar had a tear in his right ulnar collateral ligament, requiring Tommy John surgery and ending his season.