Fellow showing his years, but coping (8)
I believe the answer is:
managing
'coping' is the definition.
('manage' can be a synonym of 'cope')
'fellow showing his' is the wordplay.
'fellow' becomes 'man' (fellow can mean a man).
'showing his' becomes 'aging' (I can't justify this - if you can you should give a lot more credence to this answer).
'man'+'aging'='MANAGING'
'years but' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for managing that I've seen before include "Running; coping" , "Handling" .)