Guy going grey, coping (8)
I believe the answer is:
managing
'coping' is the definition.
('manage' can be a synonym of 'cope')
'guy going grey' is the wordplay.
'guy' becomes 'man' (guy can informally mean a man).
'going grey' becomes 'aging' (I can't justify this - if you can you should give a lot more credence to this answer).
'man'+'aging'='MANAGING'
Can you help me to learn more?
(Other definitions for managing that I've seen before include "Handling" , "Running; coping" .)