This is also the name of an Irish county, which was itself probably derived from Irish clár meaning "plank, level surface".
In England, it began to be used as a given name after the Protestant Reformation. It was moderately common in the 19th century. It began to rise in popularity again in the late 1980s, probably helped along by characters on the American television shows Friends (1994-2004) and Charmed (1998-2006). It is currently much more common in the United Kingdom, Australia and New Zealand than the United States.
A moon of Saturn bears this name, in honour of the Titan.