Chap, ancient, coped (7)
I believe the answer is:
managed
'coped' is the definition.
('manage' can be a synonym of 'cope')
'chap ancient' is the wordplay.
'chap' becomes 'man' (chap can mean a man).
'ancient' becomes 'aged' (I've seen this before).
'man'+'aged'='MANAGED'
(Other definitions for managed that I've seen before include "Supervised (staff)" , "Controlled, was in charge of" , "Coped" , "Ran, administered" , "Contrived" .)