British ultra-sloshed and barbarous (6)
I believe the answer is:
brutal
'barbarous' is the definition.
(synonyms)
'british ultra-sloshed' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'sloshed' indicates anagramming the letters.
'ultra' with letters rearranged gives 'rutal'.
'b'+'rutal'='BRUTAL'
'and' acts as a link.
(Other definitions for brutal that I've seen before include "extremely honest" , "Cruel, heartless" , "Senselessly cruel" , "Harsh, merciless" , "Inhuman - pitiless" .)