Made drunk with drink (4)
I believe the answer is:
mead
'drink' is the definition.
(mead is a kind of drink)
'made drunk' is the wordplay.
'drunk' indicates an anagram.
'made' is an anagram of 'MEAD'.
'with' is the link.
(Other definitions for mead that I've seen before include "Honeyed drink for dame" , "Honey drink; lea" , "Alcoholic drink of fermented honey and water of old" , "Alcohol" , "Old honey-based drink for dame" .)