Leasure spent the 2022 campaign split between the High–A Great Lakes Loons and Double–A Tulsa Drillers. In 49 relief outings split between the two affiliates, he accumulated a 3.38 ERA with 84 strikeouts and 7 saves across 58+2⁄3 innings pitched.[3] Leasure began the 2023 campaign with Tulsa, compiling a 3.09 ERA with 56 strikeouts and 9 saves in 29 appearances.[4]
The White Sox invited Leasure to spring training in 2024.[8] On March 27, 2024, Chicago selected Leasure's contract after he made the team's Opening Day roster.[9] While playing for Triple–A Charlotte on June 16, Leasure was part of a seven–pitcher no-hitter against the Durham Bulls.[10]