After signing with the Orioles, Hart made his professional debut that season with the Aberdeen IronBirds, going 3-1 with a 2.25 ERA in 24 relief innings pitched. In 2014 he pitched for the Delmarva Shorebirds where he was 1-3 with a 3.68 ERA in 24 relief appearances, and in 2015, he played for Delmarva, the Frederick Keys, and the Bowie BaySox, pitching to a combined 6-2 record and 1.49 ERA in 54.1 innings pitched out of the bullpen. He began 2016 with Bowie. Hart was promoted to the majors for the first time on July 14, 2016. He made his major league debut on July 17, throwing innings while earning his first career strikeout. He made two more scoreless appearances for the Orioles the next two games before being optioned back to AA Bowie on July 24. He was recalled again on August 12, where he pitched 1 perfect innings out of the bullpen. He also had one at bat in the game, striking out. On September 22, Hart allowed the first run of his career, a solo home run to Hanley Ramírez in a game against the Boston Red Sox. The home run ended Hart's streak of 18 consecutive scoreless games to start his career and his 15 scoreless innings streak also came to an end. He ended his first year in the big leagues having pitched in 22 games while tossing 18 innings and only allowing one run. Hart pitched to a 0.49 ERA and 0.98 WHIP while striking out 12 batters and issuing six walks. Hart made the Orioles Wild Card Game roster and ended up pitching to one batter, inducing a fly out to end the seventh inning. The Orioles would go on to lose in the 11th inning, 5-2. Hart made Baltimore's 2017 Opening Day roster. On April 7, Hart earned his first career major league victory. The win came against the New York Yankees after Hart retired Starlin Castro in the seventh inning and teammate Seth Smith hit a go-ahead home run in the bottom half of the inning. Hart was optioned to the Norfolk Tides and recalled to Baltimore multiple times during the season. In 13 relief appearances for Norfolk he was 1-0 with a 2.35 ERA, and in 51 appearances for Baltimore, he was 2-0 with a 3.71 ERA. Hart began the 2018 season with Norfolk. He spent most of the season in the minors, pitching in 20 games only for the Orioles. He was designated for assignment when the Orioles reclaimed Hanser Alberto on waivers on March 1, 2019.
Milwaukee Brewers
On March 7, 2019, Hart was claimed off waivers by the Los Angeles Dodgers. On April 4, he was claimed off waivers by the Milwaukee Brewers. Hart was designated for assignment on July 31, 2019.
New York Mets
On August 3, 2019, Hart was claimed off waivers by the New York Mets. He was designated to the minor leagues on August 8 after only one appearance with the Mets. Hart elected free agency following the 2019 season.
Oakland Athletics
On February 4, 2020, Hart signed a minor league deal with the Oakland Athletics.
