Some people accepting petition (4)
I believe the answer is:
plea
'petition' is the definition.
(petition can mean to plea or beg)
'some people accepting' is the wordplay.
'some' says the answer is hidden in the clue (some parts of the word are used).
'PLEA' is hidden within 'people accepting'.
(Other definitions for plea that I've seen before include "Request for mercy?" , "Humble request for help" , "response to criminal charges" , "Excuse - pretext" , "Intercession" .)