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' says the letters should be written in reverse (going up in a down clue).
'opera singer' becomes 'diva' (I've seen this before).
'diva' in reverse letter order is 'AVID'.
'and' is the link.
(Other definitions for avid that I've seen before include "Ardent about diva" , "hungry" , "Mad for diva" , "deeply enthusiastic" , "Greedy or eagerly desirous" .)