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