Live with artist, accepting vilification, in Caribbean location (7)
I believe the answer is:
bermuda
'caribbean location' is the definition.
(Caribbean island)
'live with artist accepting vilification' is the wordplay.
'live' becomes 'be' (synonyms).
'with' says to put letters next to each other.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'accepting' means one lot of letters goes inside another.
'vilification' becomes 'mud' (as in slinging mud at someone).
'ra' placed around 'mud' is 'rmuda'.
'be'+'rmuda'='BERMUDA'
'in' acts as a link.
(Other definitions for bermuda that I've seen before include "shorts originated here" , "NW Atlantic colony" , "Islands in the north-west Atlantic" , "N. Atlantic island group" , "Island group in NW Atlantic" .)