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.
This name has been used occasionally in England since the 12th century. It was not common in the English-speaking world until the end of the 20th century.
The name was brought to public attention by Samuel A. Taylor's play Sabrina Fair (1953) and the movie adaptation Sabrina that followed it the next year. This is also the name of a comic book character, Sabrina the Teenage Witch, first introduced 1962 and with television adaptations in 1970-1974 and 1996-2003, both causing minor jumps in popularity. Another jump occurred in 1976, when it was used for a main character on the television series Charlie's Angels.