Playwright needing drink at first (9)
I believe the answer is:
dramatist
'playwright' is the definition.
(I know that playwright can be written as dramatist)
'drink at first' is the wordplay.
'drink' becomes 'dram' (small alcoholic drink).
'first' becomes 'ist' (ist resembles dst).
'dram'+'at'+'ist'='DRAMATIST'
'needing' is the link.
(Other definitions for dramatist that I've seen before include "Shakespeare, say" , "Playwright" , "O'Neill or O'Casey, for example" , "man of theatre" , "Wordsmith" .)