1580s, "handy, dexterous," apparently from East Anglian dialectal cliver "expert at seizing," perhaps from East Frisian klüfer "skillful," or Norwegian dialectic klover "ready, skillful," and perhaps influenced by Old English clifer "claw, hand" (early usages seem to refer to dexterity). Or perhaps akin to Old Norse kleyfr "easy to split" and from a root related to cleave "to split." Extension to intellect is first recorded 1704.
The meaning has narrowed since, but clever also often in old use and dialect meant "well-shaped, attractive-looking" and in 19c. American English sometimes "good-natured, agreeable." Related: Cleverly; cleverness.