Parrish began the 2022 season with Northwest Arkansas and was promoted to the Triple–A Omaha Storm Chasers in June.[9] In 27 games (25 starts) between the two clubs, he registered a combined 7–11 record and 4.13 ERA with 99 strikeouts in 128+2⁄3 innings pitched.[10] In 2023, Parrish made 28 appearances (24 starts) split between Northwest Arkansas and Omaha, but struggled to a 7–8 record and 6.54 ERA with 96 strikeouts in 117.0 innings of work.[11] On September 26, 2023, Parrish was released by the Royals organization.[12]
Atlanta Braves
On November 10, 2023, Parrish signed a minor league contract with the Atlanta Braves.[13] He split the 2024 campaign between the Double-A Mississippi Braves and Triple-A Gwinnett Stripers. In 29 games (18 starts) for the two affiliates, Parrish compiled a 7-5 record and 3.28 ERA with 113 strikeouts across 115+1⁄3 innings pitched. He elected free agency following the season on November 4, 2024.[14]
Cincinnati Reds
On December 24, 2024, Parrish signed a minor league contract with the Cincinnati Reds.[15] He made 29 appearances (nine starts) split between the Triple-A Louisville Bats and Double-A Chattanooga Lookouts in 2025, accumulating a 4-5 record and 4.37 ERA with 57 strikeouts over 70 innings of work. Parrish elected free agency following the season on November 6, 2025.[16]