Invites fool to entertain king (4)
I believe the answer is:
asks
'invites' is the definition.
(I've seen this before)
'fool to entertain king' is the wordplay.
'fool' becomes 'ass' (ass is a kind of fool**).
'to entertain' is an insertion indicator.
'king' becomes 'k'.
'ass' placed around 'k' is 'ASKS'.
(Other definitions for asks that I've seen before include "Begs" , "Puts a question" , "Questions" , "Poses a question" , "Inquiries" .)