Temper where old car not starting (5)
I believe the answer is:
'temper' is the definition.
'old car not starting' is the wordplay.
'old car' becomes 'banger' (slang for an old, dilapidated vehicle).
'not starting' means to remove the first letter.
'banger' with its first letter taken away is 'ANGER'.
'where' acts as a link.
(Other definitions for anger that I've seen before include "Extreme annoyance" , "Feeling of vexation" , "Nettle" , "Emotion" , "Strongly annoy" .)