Scottish (of Norman origin): name of a powerful Scottish clan, originally a habitational name from Saint-Clair-sur-Elle in La Manche or Saint-Clair-l’Évêque in Calvados, so called from the dedication of their churches to St. Clarus (see Clare 3).
Jewish: Americanized form of some like-sounding Ashkenazic Jewish surname.
Dictionary of American Family Names, Oxford University Press, Mar 2003