He's entering wager by request (6)
I believe the answer is:
behest
'request' is the definition.
(thesaurus)
'he's entering wager' is the wordplay.
'entering' means one lot of letters goes inside another.
'wager' becomes 'bet' ('bet' can be a synonym of 'wager').
'hes' put into 'bet' is 'BEHEST'.
'by' is the link.
(Other definitions for behest that I've seen before include "Command - Thebes (anag)" , "Command, bidding" , "(At someone's) command" , "Order" .)