Overcoat has strange lustre (6)

I believe the answer is:

ulster

'overcoat' is the definition.
(I know that ulster is a type of overcoat)

'strange lustre' is the wordplay.
'strange' is an anagram indicator.
'lustre' anagrammed gives 'ULSTER'.

'has' is the link.

(Other definitions for ulster that I've seen before include "Province of Ireland; overcoat" , "Overcoat; Northern Ireland" , "Northern Ireland (loosely)" , "Loose overcoat - result (anag)" , "Area of Ireland" .)

I've seen this clue in The Sun.

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