Prostitute can't rouse drunk (9)
I believe the answer is:
courtesan
'prostitute' is the definition.
(courtesan is a kind of prostitute)
'can't rouse drunk' is the wordplay.
'drunk' indicates an anagram.
'cant'+'rouse'='cantrouse'
'cantrouse' is an anagram of 'COURTESAN'.
(Other definitions for courtesan that I've seen before include "Fanny Hill, perhaps" , "lover" , "Prostitute - mistress of high-ranking man" , "paramour" , "Kept woman" .)