Directors supporting rise of classic pub feature (9)
I believe the answer is:
dartboard
'pub feature' is the definition.
(dartboards are often found in pubs)
'directors supporting rise of classic' is the wordplay.
'directors' becomes 'board' (board of directors).
'supporting' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'rise of' says the letters should be written backwards (in a down clue, letters go up).
'classic' becomes 'trad' (abbreviation of traditional).
'trad' back-to-front is 'dart'.
'board' after 'dart' is 'DARTBOARD'.
(Other definitions for dartboard that I've seen before include "Target for arrows" , "Pub game equipment" , "Target found in pubs" , "It's doubles all round" .)