
1) Former county of England
Found on
https://www.crosswordclues.com/clue/hexhamshire

Hexhamshire was a county of Northern England. It existed for several hundred years until it was incorporated into Northumberland in 1572. ==County== The county probably originated as one of the districts of the Kingdom of Northumbria, the town of Hexham then being the seat of a bishopric. It later lost its privileges, and became considered part of...
Found on
http://en.wikipedia.org/wiki/Hexhamshire

Hexhamshire included the parishes of Hexham (including Whitley chapelry), Allendale (including West Allen or Ninebanks, Allenheads and Carr Shield chapelries), and St. John Lee. It was a part of Northumberland which was not controlled by the Bishop of Durham- instead it was owned by the Archbishop of York.
Found on
http://www.encyclo.co.uk/local/20766
No exact match found.