Endlessly pester for membership token? (5)
I believe the answer is:
badge
'membership token?' is the definition.
(members of a club might wear a badge)
'endlessly pester' is the wordplay.
'endlessly' means to remove the last letter.
'pester' becomes 'badger' (synonyms).
'badger' with its last letter taken off is 'BADGE'.
'for' acts as a link.
(Other definitions for badge that I've seen before include "Thing worn to show, say, membership of organisation" , "Identity symbol" , "Shield" , "Identifying label" , "Identifying emblem" .)