One drunk for a long time (3)
I believe the answer is:
eon
'long time' is the definition.
(eon is a kind of long time)
'one drunk' is the wordplay.
'drunk' indicates an anagram.
'one' anagrammed gives 'EON'.
'for a' is the link.
(Other definitions for eon that I've seen before include "Vast age; eternity" , "Very long period (US and technical spelling)" , "Huge time period" , "billion years" , "Geological period" .)