Influence strike (5)
I believe the answer is:
clout
I believe this is a double definition.
'influence' is the first definition.
(thesaurus)
'strike' is the second definition.
(clouting is a kind of striking)
(Other definitions for clout that I've seen before include "Smack - influence" , "Ne'er cast a ... till May be out, it's said" , "weight" , "A blow; powerful influence" , "Political influence - flat-headed nail" .)