Welsh composer abridged a short story (7)
I believe the answer is:
novella
'short story' is the definition.
(I've seen this before)
'welsh composer abridged a' is the wordplay.
'welsh composer' becomes 'novello' (I've seen this before).
'abridged' means to remove the last letter.
'novello' with its final letter taken off is 'novell'.
'novell'+'a'='NOVELLA'
(Other definitions for novella that I've seen before include "Composition" , "short book" , "story, short one" , "Slim volume of fiction" , "Slim work of fiction" .)