Greedy Biblical king losing his head (4)
I believe the answer is:
avid
'greedy' is the definition.
(synonyms)
'biblical king losing his head' is the wordplay.
'biblical king' becomes 'David' (Old Testament figure).
'losing his head' means to remove the first letter.
'david' with its initial letter taken off is 'AVID'.
(Other definitions for avid that I've seen before include "hungry" , "Very keen, desirous" , "Impassioned about diva" , "Fanatical" , "Greatly desirous" .)