Keen to behead biblical king (4)
I believe the answer is:
avid
'keen' is the definition.
(both can mean enthusiastic)
'behead biblical king' is the wordplay.
'behead' means to remove the first letter (I've seen 'beheaded' mean this (the head of the word is removed)).
'biblical king' becomes 'David' (Old Testament figure).
'david' with its initial letter removed is 'AVID'.
'to' acts as a link.
(Other definitions for avid that I've seen before include "Excessively keen" , "Keen and eager" , "Keenly enthusiastic" , "Zealous, enthusiastic" , "Impassioned about diva" .)