Temper? Old car not starting (5)
I believe the answer is:
anger
'temper?' is the definition.
(temper is a kind of anger)
'old car not starting' is the wordplay.
'old car' becomes 'banger' (I've seen this before).
'not starting' means to remove the first letter.
'banger' with its first letter taken off is 'ANGER'.
(Other definitions for anger that I've seen before include "Extreme annoyance" , "Annoyance, displeasure" , "Rage" , "wind up?" , "Fire" .)