Drink but drunkenly get going without it (6)
I believe the answer is:
eggnog
'drink' is the definition.
(I know that eggnog is a type of drink)
'drunkenly get going without it' is the wordplay.
'drunkenly' indicates an anagram.
'without' suggests deleting specific letters.
'get'+'going'='getgoing'
'getgoing' with 'it' taken out is 'gegong'.
'gegong' anagrammed gives 'EGGNOG'.
'but' is the link.
(Other definitions for eggnog that I've seen before include "Drink (milk punch)" , "Dairy-based drink" , "Kind of sweet punch" , "Rum-based drink" , "Milky winter punch" .)