Bar in American city supplying dope (5)
I believe the answer is:
ninny
'dope' is the definition.
(both can mean a foolish person)
'bar in american city' is the wordplay.
'bar' becomes 'inn' (I've seen this in other clues).
'in' is an insertion indicator.
'american city' becomes 'ny' (short for New York).
'inn' inserted into 'ny' is 'NINNY'.
'supplying' is the link.
(Other definitions for ninny that I've seen before include "dope" , "Simpleton" , "gravely so miscalled by mechanicals" , "Stupid foolish person" , "Silly billy" .)