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' indicates a hidden word.
'SOT' is hidden in the letters of 'besotted'.
(Other definitions for sot that I've seen before include "One drinks" , "Habitual drunkard" , "Habitual drinker" , "One's often intoxicated" , "Lush" .)