Rule broken round street in Irish province (6)
I believe the answer is:
ulster
'irish province' is the definition.
(one of the four provinces of Ireland)
'rule broken round street' is the wordplay.
'broken' is an anagram indicator.
'round' indicates putting letters inside.
'street' becomes 'st' (abbreviation).
'rule' anagrammed gives 'uler'.
'uler' going around 'st' is 'ULSTER'.
'in' acts as a link.
(Other definitions for ulster that I've seen before include "Six, or nine, counties" , "A heavy coat" , "Loose overcoat - result (anag)" , "Overcoat; N. Ireland" , "Overcoat; Irish region" .)