Very keen to rise as a singer (4)
I believe the answer is:
diva
'a singer' is the definition.
(diva can mean a female opera singer)
'very keen to rise' is the wordplay.
'very keen' becomes 'avid' (I've seen this before).
'to rise' shows that the letters should be reversed in order.
'avid' written backwards gives 'DIVA'.
'as' is the link.
(Other definitions for diva that I've seen before include "Avid like opera singer" , "Distinguished female singer" , "Operatic female singer" , "One who sings" , "High-maintenace woman" .)