Accepted, thanks to chap (5)
I believe the answer is:
taken
'accepted' is the definition.
('take' can be a synonym of 'accept')
'thanks to chap' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'to chap' becomes 'ken' (man's name).
'ta'+'ken'='TAKEN'
(Other definitions for taken that I've seen before include "Removed (from a place)" , "Removed, accepted" , "Transported" , "Appropriated" , "Obtained" .)