Old English clæppan "to throb, beat," common Germanic, echoic (cognate with Old Frisian klapa "to beat," Old Norse klappa, Old High German klaphon, German klappen, Old Saxon klapunga). Meaning "to strike or knock" is from c. 1300. Meaning "to make a sharp noise" is late 14c. Of hands, to beat them together to get attention or express joy, from late 14c. To clap (someone) on the back is from 1520s. Related: Clapped; clapping.
"gonorrhea," 1580s, of unknown origin, perhaps from Middle English clapper "rabbit-hole," from Old French clapoire (Modern French clapier), originally "rabbit burrow" (of uncertain origin), but 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.