Most enthusiastic king has three points established (7)
I believe the answer is:
keenest
'most enthusiastic' is the definition.
(I've seen this in another clue)
'king has three points established' is the wordplay.
'king' becomes 'K' (abbreviation for king in chess).
'has' says to put letters next to each other.
'three points' becomes 'een' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'established' becomes 'est' (abbreviation).
'k'+'een'+'est'='KEENEST'
Can you help me to learn more?
(Other definitions for keenest that I've seen before include "most piercing" , "Most interested or sharp" , "Most anxious" , "Most eager and sharp" , "most sensitive" .)