Claiborne began the 2013 season with the Scranton/Wilkes-Barre RailRiders, and was called up to the majors for the first time on May 3, 2013, when the Yankees placed Joba Chamberlain on the disabled list.[2][9] He made his major league debut on May 5, against the Oakland Athletics. During his debut, he pitched two scoreless innings without allowing a baserunner.[10] Claiborne was optioned down to Scranton/Wilkes-Barre on August 16.[11] He was then recalled to be the 26th player for a doubleheader against the Toronto Blue Jays on August 20 but was optioned back to Scranton/Wilkes-Barre right after the second game. However, he was brought back up on August 22 when infielder Jayson Nix was placed on the disabled list.[12] Claiborne was optioned back to Triple-A on August 26 when the Yankees activated Derek Jeter from the disabled list.[13] He was then brought back up to the Yankees on September 2 after the rosters expanded the previous day.[14] Claiborne was designated for assignment by the Yankees on December 19, 2014.[15]
Miami Marlins
Claiborne was claimed off waivers by the Miami Marlins on December 23, 2014.[16] He missed the entire 2015 season with a shoulder injury.[17] On March 17, 2016, Claiborne was released by the Marlins.[18]
San Francisco Giants
On May 16, 2016, Claiborne signed a minor league contract with the San Francisco Giants. He made 34 appearances out of the bullpen for the Double–A Richmond Flying Squirrels, posting a 2.38 ERA with 49 strikeouts and 3 saves. Claiborne elected free agency following the season on November 7.[19]
Texas Rangers
On February 24, 2017, Claiborne signed a minor league deal with the Texas Rangers.[20] He was promoted to the major league roster on June 22. Claiborne was designated for assignment on July 2.[21]
Cleveland Indians
On January 26, 2018, Claiborne signed a minor league contract with the Cleveland Indians.[22] In 10 appearances split between the rookie–level Arizona League Indians, Double–A Akron RubberDucks, and Triple–A Columbus Clippers, he accumulated a 9.31 ERA with 10 strikeouts across 9+2⁄3 innings pitched. Claiborne elected free agency following the season on November 2.[23]
Claiborne was named pitching coach of the Tampa Tarpons the New York Yankees Single-A affiliate for the 2024 season.
Personal life
The first time Claiborne attended a baseball game, which featured the visiting Yankees playing the Texas Rangers, his father encouraged him to play with the "class and respect" of a Yankee. His father died of a stroke during Claiborne's sophomore year at Tulane.[1] He contributes to a website, TheCupCheck.com, which is run by minor league baseball players to give other minor leaguers tips on how to handle life in professional baseball. The Wall Street Journal called Claiborne "one of the site's most prolific contributors."[24]