Run at a fee (6)
I believe the answer is:
charge
This clue is a double definition.
'run at' is the first definition.
(I've seen this in another clue)
'a fee' is the second definition.
(I've seen this before)
(Other definitions for charge that I've seen before include "money to be paid" , "Fix as a price or accuse" , "In which an offender may be given" , "Control" , "Formally accuse; rush" .)