Tune Oscar composed for mistress (9)
I believe the answer is:
courtesan
'mistress' is the definition.
(courtesan is a kind of mistress)
'tune oscar composed' is the wordplay.
'composed' indicates an anagram.
'tune'+'oscar'='tuneoscar'
'tuneoscar' anagrammed gives 'COURTESAN'.
'for' acts as a link.
(Other definitions for courtesan that I've seen before include "Kept woman" , "High-class prostitute" , "Fanny Hill, perhaps" , "paramour" , "Prostitute - mistress of high-ranking man" .)