I’m not local, and it’s a while since I’ve been there, but the answer is ‘yes’.
There’s some pretty nice singletrack on Hexham Common (the marked bridleways, from memory) that’ll do you for a couple of hours or so.
There’s also a long bridleway marked on the map running down from above Allenheads (EDIT: might have been Allendale actually) that I always wanted to check out and never did. It looked ok on Google Earth a few years back, so it’s probably worth exploring.
How far’s Edmundbyers from Hexham? About half an hour? There’s some good stuff around there on Blanchland Common.
Sorry I can’t be more help.