Jazz composed by a man in a temper (7)
I believe the answer is:
ragtime
'jazz' is the definition.
(type of jazz)
'a man in a temper' is the wordplay.
'a man' becomes 'Tim' (short for Timothy).
'in' indicates putting letters inside.
'a temper' becomes 'rage' (I have seen 'Terrible temper' mean 'rage' so perhaps 'temper' could also mean 'rage').
'tim' going within 'rage' is 'RAGTIME'.
'composed by' acts as a link.
(Other definitions for ragtime that I've seen before include "Song and dance" , "Syncopated music style" , "musical style" , "Syncopated piano music - migrate (anag)" , "Migrate to find jazz music" .)