c. 1300, "to strike with a quick, sharp motion, to slap," from Old English clæppan "to throb, beat," or from or influenced by its Old Norse cognate, klappa, a common Germanic echoic verb (compare Old Frisian klapa "to beat," Old High German klaphon, German klappen, Old Saxon klapunga).
Meaning "to make a sharp noise" is late 14c. Of hands, "to beat together to get attention or express joy," from late 14c. Without specific mention of hands, "to applaud, to manifest approbation by striking the hands together," 1610s. To clap (someone) on the back is from 1520s and retains the older sense. Related: Clapped; clapping.
"a sudden, sharp, loud noise," c. 1200, from clap (v.). Of thunder, late 14c. Meaning "sudden blow" is from c. 1400; meaning "noise made by slapping the palms of the hands together" is from 1590s.
"gonorrhea," 1580s, of unknown origin, perhaps from Middle English clapper "rabbit-hole," from Old French clapoire (Modern French clapier), originally "rabbit burrow" (a word of uncertain origin), given a slang extension to "brothel" and also the name of a disease of some sort. In English originally also a verb, "to infect with clap." Related: Clap-doctor.