Modest having to accept trophy and fame (9)
I believe the answer is:
spotlight
'fame' is the definition.
(I've seen this before)
'modest having to accept trophy' is the wordplay.
'modest' becomes 'slight'.
'having to accept' indicates putting letters inside.
'trophy' becomes 'pot' (type of trophy).
'slight' enclosing 'pot' is 'SPOTLIGHT'.
'and' acts as a link.
(Other definitions for spotlight that I've seen before include "Stage actor may be in it" , "Direct attention to" , "Illuminate" , "Prominent position" , "Give prominence to" .)