Republican overwhelmed by giant drink (4)
I believe the answer is:
grog
'drink' is the definition.
(I know that grog is a type of alcoholic beverage)
'republican overwhelmed by giant' is the wordplay.
'republican' becomes 'R' (abbreviation).
'overwhelmed by' means one lot of letters goes inside another (inserted letters get absorbed or overwhelmed).
'giant' becomes 'gog' (I've seen this in other clues).
'r' put into 'gog' is 'GROG'.
(Other definitions for grog that I've seen before include "Drink of spirits and water liked by sailors" , "Old naval drink" , "Nautical drink" , "Sailors' drink of rum and water" , "Spirits and water mixture" .)