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Bubic, 25, is 0-2 with a 3.94 ERA in three starts this season. He has struck out 16 and walked two batters through 16 innings.
He is 10-28 with a 4.85 ERA in 70 games (60 starts) since making his debut with the Royals in 2020.
Kansas City recalled left-hander Josh Taylor from Triple-A Omaha in a corresponding move.
Taylor, 30, last pitched in the majors in 2021 with the Boston Red Sox. He has a 6.75 ERA with no decisions in five relief appearances this season at Omaha.