Pretend to have influence (6)
I believe the answer is:
affect
This clue is a double definition.
'pretend to' is the first definition.
(thesaurus)
'influence' is the second definition.
(I know that influence is a more specific form of the action affect)
'have' is the link.
(Other definitions for affect that I've seen before include "front" , "Make impression on or arouse sympathy in" , "It always has a cause" , "impress" , "Touch (feelings); pretend (to feel)" .)