One coming out demanding dismissal of fellow composer (7)
I believe the answer is:
debussy
'composer' is the definition.
(Claude Debussy)
'one coming out demanding dismissal of fellow' is the wordplay.
I cannot really see how this works, but
'one coming out' could be 'deb' (I've seen this before) and 'deb' is located in the answer.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for debussy that I've seen before include "Note-writer" , "Claude -, Fr. composer" , "Claude, impressionist composer" , "Claude -, C. nineteen-twenty French composer" , "Clair de Lune composer" .)