As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.
In the United States it became more common for girls in the early 1980s, shortly after the debut of the television sitcom The Facts of Life (1979-1988), which featured a character named Blair Warner. The name left the American top 1000 rankings two decades later, but was resurrected by another television character, this time Blair Waldorf from the series Gossip Girl (2007-2012).