Coat with exceptional lustre (6)
I believe the answer is:
ulster
'coat' is the definition.
(ulster is a kind of coat)
'exceptional lustre' is the wordplay.
'exceptional' indicates an anagram.
'lustre' anagrammed gives 'ULSTER'.
'with' is the link.
(Other definitions for ulster that I've seen before include "Six, or nine, counties" , "Odd result for the North" , "Overcoat; Irish region" , "Long loose overcoat, from the province?" , "Overcoat; N. Ireland" .)