Fellow, mature, is to cope (6)
I believe the answer is:
manage
'is to cope' is the definition.
(I've seen this before)
'fellow mature' is the wordplay.
'fellow' becomes 'man' (I've seen this before).
'mature' becomes 'age' (synonyms).
'man'+'age'='MANAGE'
(Other definitions for manage that I've seen before include "Control, direct, run" , "Be in charge of something" , "Contrive" , "Take control" , "Run, administer" .)