Accept bet son refused (4)
I believe the answer is:
take
'accept' is the definition.
(to accept is to take possession of)
'bet son refused' is the wordplay.
'bet' becomes 'stake' (staking is a kind of betting).
'son' becomes 's' (genealogical abbreviation for son).
'refused' indicates named letters should be taken away.
'stake' with 's' taken away is 'TAKE'.
(Other definitions for take that I've seen before include "Grab" , "Receive; subtract" , "Remove; consume" , "Seize; purloin" , "catch" .)