Very keen leader dismissed by king of Israel (4)
I believe the answer is:
avid
'very keen' is the definition.
(I've seen this before)
'leader dismissed by king of israel' is the wordplay.
'leader' says to take the initial letters.
'by' is a charade indicator (letters next to each other).
'king of israel' becomes 'avi' (I can't justify this - if you can you should give a lot more credence to this answer).
The initial letter of 'dismissed' is 'd'.
'd' after 'avi' is 'AVID'.
Can you help me to learn more?
(Other definitions for avid that I've seen before include "Eager like diva" , "Mad for diva" , "Greedy like diva" , "In operation" , "Showing active interest and enthusiasm" .)