Last drop of moonshine in fairly new still (7)
I believe the answer is:
quieten
'still' is the definition.
(I know that still can be written as quieten)
'last drop of moonshine in fairly new' is the wordplay.
'last drop of' suggests the final letters.
'in' means one lot of letters goes inside another.
'fairly' becomes 'quite' (I've seen this before).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
The last letter of 'moonshine' is 'e'.
'e' inserted inside 'quite' is 'quiete'.
'quiete'+'n'='QUIETEN'
(Other definitions for quieten that I've seen before include "Hush" , "Make calm" , "Silence" .)