County right to cut store's lease (10)
I believe the answer is:
shropshire
'county' is the definition.
(I know that Shropshire is a county)
'right to cut store's lease' is the wordplay.
'right' becomes 'r' (common abbreviation).
'to cut' is an insertion indicator (some letters cut their way into a word).
'store's' becomes 'shop's' ('shop' can be a synonym of 'store').
'lease' becomes 'hire' (synonyms).
'r' going inside 'shops' is 'shrops'.
'shrops'+'hire'='SHROPSHIRE'
(Other definitions for shropshire that I've seen before include "county" , "largely rural location" , "Region of England" .)