Coward might have written this answer after drink (5)
I believe the answer is:
drama
'coward might have written this' is the definition.
(Noel Coward was a playwright)
'answer after drink' is the wordplay.
'answer' becomes 'a' (abbreviation eg in Q and A).
'after' means one lot of letters go next to another.
'drink' becomes 'dram' (I've seen this before**).
'a' after 'dram' is 'DRAMA'.
(Other definitions for drama that I've seen before include "Play - big emotional scene" , "Play - excitement" , "Acting" , "Play; emotional event" , "Theatrical performance" .)