Objections over cigarette end (4)
I believe the answer is:
stub
'cigarette end' is the definition.
(I've seen this before)
'objections over' is the wordplay.
'objections' becomes 'buts' (I've seen this before).
'over' is a reversal indicator.
'buts' written backwards gives 'STUB'.
(Other definitions for stub that I've seen before include "evidence of smoking, for example" , "Pencil/cigarette remnant" , "Butt of pencil or cigarette" , "what smoker drops in street?" , "30 [FAG END]" .)