Fellow player's agent (6)
I believe the answer is:
factor
'agent' is the definition.
(business term for a representative)
'fellow player's' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'player' becomes 'actor' (synonyms).
'f'+'actor'='FACTOR'
(Other definitions for factor that I've seen before include "Level on sun-screen scale" , "Number by which another is exactly divisible" , "Contributory influence; business agent" , "Circumstances" , "Reason" .)