One of two giants swigging first of rum — a diluted type (4)
I believe the answer is:
grog
'a diluted type' is the definition.
(drink of spirit diluted with water)
'one of two giants swigging first of rum' is the wordplay.
'one of two giants' becomes 'gog' (Gog and Magog are mythical giants).
'swigging' is an insertion indicator.
'first of rum' becomes 'r' (1st letter of 'rum').
'gog' going around 'r' is 'GROG'.
(Other definitions for grog that I've seen before include "Old naval drink" , "Spirits and water mixture" , "Mixture of spirit and water" , "Booze" , "Nautical drink" .)