Pieces of peach stone are a nuisance (4)

I believe the answer is:

pest

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'a nuisance' is the definition.
(I've seen this before)

'pieces of peach stone are' is the wordplay.
'pieces of' indicates taking the first letters.
'stone are' becomes 'est' (I can't justify this - if you can you should give a lot more credence to this answer).
The initial letter of 'peach' is 'p'.
'p'+'est'='PEST'

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(Other definitions for pest that I've seen before include "Constant nuisance" , "Nuisance; half a European capital" , "Troublesome man or animal" , "Annoying thing" , "A nuisance - step on it" .)

I've seen this clue in the Evening Standard.

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