Sims played the 2013 season with the Single–A Rome Braves. He started the season in the bullpen but was then moved to the rotation.[4][5] He finished the season 12–4 with a 2.62 ERA and 134 strikeouts in 116+2⁄3 innings. In 2013, Sims was considered the Braves best prospect according to MLB.com.[6]
In 2014 he was 8–11 with a 4.20 ERA for the High–A Lynchburg Hillcats.[7] He had fallen to third on the same list by the start of the 2015 season,[8] and was placed seventh on the year-end list.[9] Between three teams, he was 7–6 with a 4.37 ERA. The Braves sent Sims to the Arizona Fall League in 2015. He opened the AFL season for the Peoria Javelinas,[10] and also started the Fall Stars Game.[11]
Sims started 2016 as the Braves # 13 prospect according to Baseball America, and was invited to spring training for the first time.[12][13] He began the season with the Mississippi Braves,[14] and was promoted to Gwinnett on April 23.[15] He struggled in the International League and returned to Mississippi on June 17.[16] Sims finished 2016 with a 7–11 record and a 4.40 ERA; his 92 walks were the fourth-highest total in the minor leagues, and more than the total of any major leaguer.[17][18][19] The Braves added him to their 40-man roster after the season.[20]
Sims faced the Los Angeles Dodgers on August 1, 2017, in his major league debut. He pitched six innings, yielding three earned runs and recording three strikeouts.[21] The debuts of Sims and Ozzie Albies marked the first time since 1968 that the Atlanta Braves started two players making their first major league appearance on the same day.[22] He finished the season 3–6, with a 5.62 ERA. In December 2017, Braves manager Brian Snitker said that he might look at Max Fried, Sims, or another pitcher as the team's fifth starter in 2018.[23] Sims spent time with the major league team in spring training, but began the 2018 season in Gwinnett.[24]
Sims started his first game as a Red on May 28, 2019, against the Pittsburgh Pirates.[27] In 2019, he made 24 appearances for Cincinnati, posting a 2–1 record and 4.60 ERA with 57 strikeouts in 43 innings pitched. In 2020, Sims went 3–0 with a 2.45 ERA and 34 strikeouts in 25+2⁄3 innings over 20 games in relief. In 2021, he went 5–3 with a 4.40 ERA and 76 strikeouts in 47 innings.
Sims earned some notoriety for his actions during a home game against the Arizona Diamondbacks in April 2021. The umpires let the game continue despite rain which would normally be enough to cause a delay. Sims couldn't get a proper grip on the wet ball, and finally forced the issue, asking home plate umpire Jerry Meals for a new baseball, and then another, and another, and another, saying each was too wet to use. Meals finally gave in and called a rain delay.[28]
In 2022, Sims appeared in 9 games for the Reds, struggling to a 9.45 ERA with 5 strikeouts in 6+2⁄3 innings pitched.[29] He was originally placed on the injured list with a back injury on May 12, 2022,[30] then transferred to the 60-day injured list on June 17.[31] On July 2, Sims underwent season-ending surgery to address a herniated disc in his back.[29][32] He returned from the injury in April 2023.[33] In 67 appearances out of the bullpen, Sims compiled a 7–3 record and 3.10 ERA with 72 strikeouts across 61 innings pitched.[34]
Sims made 43 appearances for Cincinnati, recording a 3.57 ERA with 40 strikeouts over 35+1⁄3 innings of work.[35]
Boston Red Sox
On July 30, 2024, the Reds traded Sims to the Boston Red Sox, in exchange for minor league pitcher Ovis Portes.[36]