Make a show of influence (6)
I believe the answer is:
affect
I believe this is a triple definition!
'make' is the first definition.
(thesaurus)
'a show' is the second definition.
(thesaurus)
'of' acts as a link.
'influence' is the third definition.
(thesaurus)
(Other definitions for affect that I've seen before include "Make impression on or arouse sympathy in" , "Arouse sadness or sympathy like tear-jerker" , "Pretend to feel or arouse sadness" , "Have impact upon" , "It always has a cause" .)