Hembree played baseball and football at Broome High School . Hembree was a standout pitcher and quarterback for Broome, but didn't pitch as a senior in 2007 due to a knee injury suffered playing football. Instead, Hembree was a designated hitter his senior season hit .320. After high school, Hembree attended the University of South Carolina , but only had one pitching appearance his entire freshman season in 2008, and transferred to the NJCAA Spartanburg Methodist College . As a transfer sophomore, he went 7-0 with a 1.22 ERA. After receiving a scholarship to the College of Charleston , Hembree transferred there, where he spent his final season of college before being drafted in the fifth round of the 2010 MLB Draft by the San Francisco Giants .  
San Francisco Giants
Hembree began his professional career in 2010, pitching in rookie league for the Arizona League Giants and going 0–0 with a 0.82 ERA over 12 appearances, with 22 strikeouts and 3 saves in 11 innings. He began the 2011 season pitching for the San Jose Giants and was promoted to the Richmond Flying Squirrels in late June. For 2011, he went a combined 1–1 with a 1.86 ERA over 54 appearances, with 78 strikeouts and 38 saves in 53 1/3 innings.
Hembree was called up to the majors for the first time on September 3, 2013. 
Boston Red Sox
Hembree was traded to the Boston Red Sox , along with Edwin Escobar , for Jake Peavy on July 26, 2014.  He made his Red Sox debut on August 9 wearing number 38 and pitching 4 Innings in relief against the Los Angeles Angels of Anaheim giving up two hits, two walks and striking out two. Due to the Red Sox Signing Cuban outfielder Rusney Castillo on August 23 and guaranteeing Castillo the uniform number 38 he wore in Cuba, Hembree switched his uniform number to 37.