Drink at first for playwright (9)
I believe the answer is:
dramatist
'playwright' is the definition.
('dramatist' can be a synonym of 'playwright')
'drink at first' is the wordplay.
'drink' becomes 'dram' (I've seen this before**).
'first' becomes 'ist'.
'dram'+'at'+'ist'='DRAMATIST'
'for' is the link.
(Other definitions for dramatist that I've seen before include "One who writes plays" , "Pinter, say" , "Coward, for example" , "Shakespeare, say" , "man of theatre" .)