He was the fifth generation of his family in America, descended from William Claiborne who had settled in Virginia in 1621. He is the father of John Claiborne and Thomas Claiborne (1780–1856), uncle of Nathaniel Herbert Claiborne and William Charles Cole Claiborne, granduncle of John Francis Hamtramck Claiborne, and great-great-great-great granduncle of Corinne Claiborne Boggs. He was elected to the Third Congress and reelected as a Republican to the Fourth and Fifth Congresses.
His bid for reelection in 1798 was unsuccessful, but he was again elected as a Republican to the Seventh and Eighth Congresses.
He died on his estate in Brunswick County in 1812.
Claiborne was a member of the State house of delegates (1783–1788), served as colonel in command of the Brunswick County Militia in 1789, sheriff of Brunswick County (1789–1792), and a member of the state senate (1790–1792).