Denies one's corking drinks (7)
I believe the answer is:
disowns
'denies' is the definition.
'one's corking drinks' is the wordplay.
'one's' becomes 'is' (Roman numeral).
'corking' means one lot of letters goes inside another (to cork can mean to plug a hole in something).
'drinks' becomes 'downs' (downing is a kind of drinking**).
'is' inserted within 'downs' is 'DISOWNS'.
(Other definitions for disowns that I've seen before include "Refuses to acknowledge" , "Has nothing to do" .)