Playwright has small drink, at first (9)
I believe the answer is:
dramatist
'playwright' is the definition.
(I know that playwright can be written as dramatist)
'small drink at first' is the wordplay.
'small drink' becomes 'dram' (I've seen this before).
'first' becomes 'ist' (ist resembles 1st).
'dram'+'at'+'ist'='DRAMATIST'
'has' acts as a link.
(Other definitions for dramatist that I've seen before include "Wordsmith" , "Coward, for example" , "man of theatre" , "Coward perhaps" , "Playwright" .)