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.
Old English clawian "to scratch, claw," from the same root as claw (n.). Related: Clawed; clawing. Compare Dutch klaauwen, Old High German klawan, German klauen.
To claw back"regain by great effort" is from 1953; as a noun, an act of this, from 1969. Earlier clawback (n.) meant "one who fawns on another, a sycophant" (1540s), from phrase claw the back "flatter, curry favor" (late 14c.); compare the more recent expression scratch (someone's) back in a similar sense.