Piece left behind when objections overturned (4)
I believe the answer is:
stub
'piece left behind' is the definition.
(eg a cigarette stub)
'objections overturned' is the wordplay.
'objections' becomes 'buts' (I've seen this before).
'overturned' shows that the letters should be reversed in order.
'buts' in reverse letter order is 'STUB'.
'when' acts as a link.
(Other definitions for stub that I've seen before include "Pencil or cigarette end" , "Put out" , "Short end" , "Remnant, butt" , "Small piece, especially of something cut down or worn away" .)