Shaw, via Mulligan, jazzed up English composer (7,8)
I believe the answer is:
vaughan williams
'english composer' is the definition.
(I've seen this before)
'shaw via mulligan jazzed up' is the wordplay.
'jazzed up' indicates an anagram.
'shaw'+'via'+'mulligan'='shawviamulligan'
'shawviamulligan' is an anagram of 'VAUGHAN WILLIAMS'.
(Other definitions for vaughan williams that I've seen before include "English composer" , "scorer" .)