Influence of Fulham’s first player (6)
I believe the answer is:
factor
'influence' is the definition.
(I've seen this before)
'fulham's first player' is the wordplay.
'fulham's first' becomes 'f' (1st letter of 'fulham').
'player' becomes 'actor' (synonyms).
'f'+'actor'='FACTOR'
'of' acts as a link.
(Other definitions for factor that I've seen before include "something that may affect result" , "Thirteen is one of fifty two" , "say, 4 of 100" , "Level on sun-screen scale" , "Component, element" .)