Composer's ecstasy (5)
I believe the answer is:
bliss
I believe this clue is a double definition.
'composer's' is the first definition.
(British composer Arthur Bliss)
'ecstasy' is the second definition.
(I've seen this in another clue)
(Other definitions for bliss that I've seen before include "One who wrote music" , "Rabbit" , "rhapsody?" , "of composing?" , "Sir Arthur --, British composer" .)