Power, influence (5)
I believe the answer is:
clout
I believe this clue is a double definition.
'power' is the first definition.
(I've seen this before)
'influence' is the second definition.
(I've seen this in another clue)
(Other definitions for clout that I've seen before include "Influence or power" , "hit hard" , "Old-fashioned garment" , "Cast not one before May is out" , "weight" .)