Stop this writer's influence (9)
I believe the answer is:
determine
'influence' is the definition.
(I know that influence can be written as determine)
'stop this writer's' is the wordplay.
'stop' becomes 'deter' (to deter behaviour is to stop it).
'this writer's' becomes 'mine' (belonging to the crossword setter).
'deter'+'mine'='DETERMINE'
(Other definitions for determine that I've seen before include "Decide - to settle" , "Ascertain by research or calculation" , "conclusion" , "I'm entered, so find our precisely" , "Learn" .)