Objections about this fag end? (4)
I believe the answer is:
stub
'this fag end?' is the definition.
(I've seen this before)
'objections about' is the wordplay.
'objections' becomes 'buts' (as in 'no ifs, no buts').
'about' says the letters should be written backwards.
'buts' in reverse letter order is 'STUB'.
(Other definitions for stub that I've seen before include "Short end" , "this pollution by smoker?" , "Short bit of pencil, say" , "Strike against hard object - one's toe, perhaps" , "Truncated remnant" .)