Composer left in temper when rejected (5)
I believe the answer is:
elgar
'composer' is the definition.
(I've seen this before)
'left in temper when rejected' is the wordplay.
'left' becomes 'l' (common abbreviation).
'in' is an insertion indicator.
'temper' becomes 'rage' (I have seen 'Terrible temper' mean 'rage' so perhaps 'temper' could also mean 'rage').
'when rejected' says the letters should be written backwards.
'l' inserted inside 'rage' is 'ragle'.
'ragle' backwards is 'ELGAR'.
(Other definitions for elgar that I've seen before include "He scored" , "Enigma Vars. composer" , "13 composer, 1857-1934" , "Enigma Variations composer" , "The 18 [APOSTLES] creator" .)