Applaud many a piano piece (4)

I believe the answer is:

clap

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'applaud' is the definition.
(synonyms)

'many a piano piece' is the wordplay.
'many' becomes 'c' (C is the Roman numeral for l00).
'a piano piece' becomes 'lap' (lap is a kind of piece. I am not sure about the 'piano' bit.).
'c'+'lap'='CLAP'

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(Other definitions for clap that I've seen before include "Strike hands together to applaud" , "Audibly show approval" , "cheer" , "Express approbation with the hands" , "Pat" .)

I've seen this clue in the Evening Standard.

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