A rising opera singer and very keen (4)
I believe the answer is:
avid
'very keen' is the definition.
(I've seen this before)
'a rising opera singer' is the wordplay.
'a rising' shows that the letters should be reversed in order (in a down clue, letters go up).
'opera singer' becomes 'diva' (I've seen this in another clue).
'diva' back-to-front is 'AVID'.
'and' acts as a link.
(Other definitions for avid that I've seen before include "Ardent about diva" , "hungry" , "Mad for diva" , "deeply enthusiastic" , "Greedy or eagerly desirous" .)