Fire it off after a quiet drink (8)
I believe the answer is:
aperitif
'drink' is the definition.
(aperitif is a kind of drink)
'fire it off after a quiet' is the wordplay.
'off' is an anagram indicator.
'after' means one lot of letters go next to another.
'a quiet' becomes 'ap' (I've seen this in other clues**).
'fire'+'it'='fireit'
'fireit' is an anagram of 'eritif'.
'eritif' after 'ap' is 'APERITIF'.
(Other definitions for aperitif that I've seen before include "it leads to blow-out" , "appetizer" , "alcohol before meal" , "Pre-meal appetiser" , "Alcoholic drink before a meal, like sherry" .)