He has previously played in MLB for the San Diego Padres, Cleveland Indians / Guardians, and Colorado Rockies.

[1] In his sophomore year, Quantrill posted a 2–0 record and 1.93 ERA in 182⁄3 innings pitched before his season was cut short by an arm injury.

[1] Heading into the 2016 Major League Baseball draft, Quantrill was ranked as one of the top available players by MLB.

Quantrill spent 2017 with both the San Antonio Missions and the Lake Elsinore Storm where he posted a combined 7–10 record with a 3.80 ERA in 22 games started between both teams.

On August 31, 2020, the Padres traded Quantrill, along with Austin Hedges, Josh Naylor, and minor league players Gabriel Arias, Owen Miller, and Joey Cantillo to the Cleveland Indians for Mike Clevinger, Greg Allen, and Matt Waldron.

[11] With the 2020 Cleveland Indians, Quantrill appeared in eight games, compiling a 0–0 record with 1.84 ERA and 13 strikeouts in 14+2⁄3 innings pitched.

[17] On November 17, 2023, the Guardians traded Quantrill to the Colorado Rockies in exchange for minor league catcher Kody Huff.