Pretend to influence (6)
I believe the answer is:
affect
I believe this is a double definition.
'pretend to' is the first definition.
(thesaurus)
'influence' is the second definition.
(thesaurus)
(Other definitions for affect that I've seen before include "Impact, have a bearing on" , "Arouse sadness or sympathy like tear-jerker" , "Make a difference to" , "Influence; make pretence of" , "Pretend - to have influence on events" .)