The meaning of clap in these idioms is somewhat removed from the original one of make a sudden explosive sound. Overtime the word developed the additional sense of make a sudden action without necessarily implying any sound.
Related Idioms :
clap eyes on
see – informal
1992 - Barry Unsworth - Sacred Hunger - If we go by the indications of the play, these two charmers have never clapped eyes on a man before, never flirted, never known the sweets of love.
clap hold of
grab someone or something roughly or abruptly - informal