Thanks a chap's not given (5)
I believe the answer is:
taken
'not given' is the definition.
('take' is the opposite to 'give')
'thanks a chap's' is the wordplay.
'thanks' becomes 'ta' (UK informal version of 'thank you').
'a chap' becomes 'ken' (man's name).
'ta'+'ken'='TAKEN'
(Other definitions for taken that I've seen before include "Appropriated" , "Transported" , "Charmed" , "Captured" , "Stolen; occupied" .)