Writer admits art is dubious (9)
I believe the answer is:
dramatist
'writer' is the definition.
(dramatist is a kind of writer)
'admits art is dubious' is the wordplay.
'is dubious' indicates an anagram.
'admits'+'art'='admitsart'
'admitsart' with letters rearranged gives 'DRAMATIST'.
(Other definitions for dramatist that I've seen before include "Playwright" , "Wordsmith" , "Coward perhaps" , "Shakespeare, say" , "man of theatre" .)