Singer keen to rise (4)
I believe the answer is:
diva
'singer' is the definition.
(diva is a kind of singer)
'keen to rise' is the wordplay.
'keen' becomes 'avid' (I've seen this in other clues).
'to rise' says the letters should be written backwards.
'avid' written backwards gives 'DIVA'.
(Other definitions for diva that I've seen before include "Long narrow top" , "Celebrated female operatic star" , "Grand female singer" , "Great singer" , "For example Sutherland" .)