Obscure American in tipsy bar set (8)
I believe the answer is:
abstruse
'obscure' is the definition.
(synonyms)
'american in tipsy bar set' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'in' indicates putting letters inside.
'tipsy' indicates an anagram.
'bar'+'set'='barset'
'barset' with letters rearranged gives 'abstre'.
'us' going within 'abstre' is 'ABSTRUSE'.
(Other definitions for abstruse that I've seen before include "Hard to understand, perhaps profound" , "Strange busts are difficult to understand" , "Difficult to comprehend" , "Esoteric" , "Obscure or recondite" .)