Run for a fee (6)
I believe the answer is:
charge
I believe this clue is a double definition.
'run' is the first definition.
'for a fee' is the second definition.
(I've seen this in another clue)
(Other definitions for charge that I've seen before include "Ask for" , "Price asked; fill" , "Demand in payment" , "Accuse; load, fill" , "Rush forward in attack" .)