Eagerly desirous (4)
I believe the answer is:
avid
'eagerly desirous' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for avid that I've seen before include "Showing active interest and enthusiasm" , "Keen or greedy" , "Mad for diva" , "Greedy like diva" , "Impassioned about diva" .)