Broken stub, possibly (4)
I believe the answer is:
bust
'broken' is the definition.
(I've seen this before)
'stub possibly' is the wordplay.
'possibly' is an anagram indicator.
'stub' with letters rearranged gives 'BUST'.
(Other definitions for bust that I've seen before include "Broken - bankrupt - sculpture" , "Head-and-shoulders sculpture" , "in pieces!" , "Bosom - ruined" , "8 across" .)