Peter out with tough conservative (3-4)
I believe the answer is:
die-hard
'conservative' is the definition.
(I've seen this before)
'peter out with tough' is the wordplay.
'peter out' becomes 'die' (I've seen this in another clue).
'with' means one lot of letters go next to another.
'tough' becomes 'hard' (similar in meaning).
'die'+'hard'='DIE-HARD'
(Other definitions for die-hard that I've seen before include "1988 Bruce Willis film" , "Obstinate or dauntless person" , "One who won't accept novelty" , "Strong opponent of change" , "One strongly opposing change; I'd heard (anag.)" .)