Besotted with drinker (3)
I believe the answer is:
sot
'drinker' is the definition.
(I know that sot is a type of drinker)
'besotted with' is the wordplay.
'with' says the answer is hidden in the clue.
'SOT' can be found hidden inside 'besotted'.
(Other definitions for sot that I've seen before include "One drinks" , "Habitual drunkard" , "Habitual drinker" , "One's often intoxicated" , "Lush" .)