[4] Clase was assigned to the Spokane Indians of the Low–A Northwest League, and finished the 2018 season after going 1–1 with a 0.64 ERA, 27 strikeouts, and 12 saves in 28+1⁄3 innings.

[3] On April 23, he was promoted to the Frisco RoughRiders of the Double-A Texas League, and went 1–2 with a 3.35 ERA and 39 strikeouts over 37+2⁄3 innings.

[11] On December 15, 2019, the Rangers traded Clase and Delino DeShields Jr. to the Cleveland Indians in exchange for Corey Kluber and cash considerations.

After converting all six save opportunities in August and holding opposing batters to a .095 average, he was named AL Reliever of the Month.

He pitched the ninth inning for the American League at Dodger Stadium and struck out the side to get the save and secure a 3–2 victory.

[2] In Game 2 of the 2024 ALDS, Clase gave up a game-winning three-run home run in the ninth inning to Detroit Tigers slugger Kerry Carpenter.

[22] In Game 3 of the 2024 ALCS, Clase gave up back-to-back home runs in the top of the 8th inning to New York Yankees sluggers Aaron Judge followed by Giancarlo Stanton.

[25][26] He has demonstrated an exceptional ability to control his pitches despite throwing at such a high velocity, averaging just 1.6 walks per 9 innings as of September 17, 2024.