Curiously his reputation ultimately grew as a composer (8)
I believe the answer is:
gershwin
'a composer' is the definition.
(I've seen this before)
'curiously his reputation ultimately grew' is the wordplay.
'curiously' is an anagram indicator.
'ultimately' suggests the final letters.
The last letter of 'reputation' is 'n'.
'his'+'n'+'grew'='hisngrew'
'hisngrew' with letters rearranged gives 'GERSHWIN'.
'as' is the link.
(Other definitions for gershwin that I've seen before include "US composer" , "George and Ira ..., American musical brothers" , "Ira and George, US brother composers" , "Scorer" , "he noted" .)