Stewart returned to the Quakes to begin the 2016 season[8] and was promoted to the Tulsa Drillers of the Texas League[9] and Oklahoma City Dodgers of the Pacific Coast League during the season.[10] Despite his promotion he was named to the mid-season Texas League all-star game.[11] He was later named the Dodgers organizational minor league pitcher of the year for 2016.[12] Between three minor league levels in 2016, he was 9–4 with a 1.79 ERA and 129 strikeouts in 21 starts.[7]
Stewart was called up to the majors on June 29, 2016, to start for the Dodgers against the Milwaukee Brewers.[13] He allowed five runs in the second inning and lost the game. He struck out seven and allowed eight hits in his five innings of work.[14] He recorded his first major league win on September 7 against the Arizona Diamondbacks when he allowed only one run in five innings.[15] Stewart made five starts and two relief appearances for the Dodgers with a 5.79 ERA in 28 innings.[16]
Stewart suffered from tendinitis in his right shoulder during spring training in 2017, causing him to begin the season on the disabled list.[17] After recovering from his injury, Stewart spent 2017 bouncing between the minors and the majors, appearing in 17 games (with 4 starts) for the Dodgers with a 3.41 ERA and no decisions[18] and also making 5 starts for Oklahoma City, where he had a 3.12 ERA.[7] On September 2, he was placed on the 60-day disabled list to make room for Rocky Gale.[19]
Toronto Blue Jays
On July 31, 2019, Stewart was claimed off waivers by the Toronto Blue Jays.[20] He was called up to the Blue Jays from Buffalo on August 5.[21] On October 30, Stewart was removed from the 40–man roster and sent outright to the Triple–A Buffalo Bisons.
Chicago Cubs
On December 12, 2019, Stewart was selected by the Chicago Cubs in the minor league phase of the 2019 Rule 5 draft.[22] Stewart did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.[23] He was released on May 28, 2020.[24]
He spent the remainder of the 2020 season with the independent Chicago Deep Dish.[25] During the 2020 offseason, Stewart completed a program with Tread Athletics that increased the velocity of his pitches.[26]
Los Angeles Dodgers (second stint)
On December 11, 2020, Stewart signed a minor league contract with the Los Angeles Dodgers organization.[27] However he underwent Tommy John surgery in May and did not pitch in 2021.[28]
Minnesota Twins
On July 14, 2022, Stewart announced that he had signed a two-year minor league contract with the Minnesota Twins.[29] In 11 games split between the Triple-A St. Paul Saints, High-A Fort Myers Miracle, and rookie-level Florida Complex League Twins, Stewart posted a cumulative 0-2 record and 7.71 ERA with 16 strikeouts in 14 innings pitched.
He began the 2023 season with Triple-A St. Paul, appearing in 7 games and registering a 2.08 ERA with a whopping 17 strikeouts in 8+2⁄3 innings of work. On April 25, 2023, Stewart had his contract selected to the active roster.[30][31] He posted a stellar 0.70 ERA with 35 strikeouts in 25+2⁄3 innings before he was placed on the injured list with right elbow soreness on June 27.[32] On August 4, Stewart was transferred to the 60–day injured list.[33] He was activated from the injured list on September 26,[34] and made three scoreless appearances to end the season.
Stewart began the 2024 campaign out of the Twins' bullpen, compiling an 0.68 ERA with 17 strikeouts over his first 13 appearances. He was placed on the injured list with right shoulder tendinitis on May 3, 2024.[35] After receiving a platelet-rich plasma injection,[36] Stewart was transferred to the 60–day injured list on July 3.[37] He was activated on July 24.[38] However, on August 9, it was announced that Stewart would miss the remainder of the season after undergoing arthroscopic shoulder surgery.[39]