Keen sort of diva (4)
I believe the answer is:
avid
'keen' is the definition.
(both can mean enthusiastic)
'sort of diva' is the wordplay.
'sort of' indicates an anagram.
'diva' anagrammed gives 'AVID'.
(Other definitions for avid that I've seen before include "Ardent about diva" , "Very keen, desirous" , "Mad for diva" , "Keenly enthusiastic" , "Greatly desirous" .)