Influence is possessed by established writer (8)
I believe the answer is:
essayist
'writer' is the definition.
(I know that essayist is a type of writer)
'influence is possessed by established' is the wordplay.
'influence' becomes 'say' (I've seen this in another clue).
'possessed by' indicates putting letters inside.
'established' becomes 'est' (abbreviated used in shop signs).
'say'+'is'='sayis'
'sayis' put into 'est' is 'ESSAYIST'.
(Other definitions for essayist that I've seen before include "Writer of shorter pieces" , "kind of writer" , "Bacon maybe" , "Writer such as Addison" , "I write" .)