Firmly established after study of artist (9)
I believe the answer is:
constable
'artist' is the definition.
(I've seen this before)
'firmly established after study' is the wordplay.
'firmly established' becomes 'stable' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'study' becomes 'con' (I've seen this before).
'stable' after 'con' is 'CONSTABLE'.
'of' acts as a link.
(Other definitions for constable that I've seen before include "PC" , "CARRY ON FILM" , "In England, a great painter or lowly policeman" , "Copper - artist" , "in blue?" .)