Hello
A very small corner of the mine is accessible but it's on enclosed private land & I'm not sure what the access situation is so I'd prefer not to say too much online.
There are two clubs actively exploring on the North York Moors and I'd suggest dashing off an email to one of those as they may be able to help. Contact email addresses should be on their respective websites. Take the time to say a word or two about yourself when doing so however, it'll invariably provoke a more helpful response!
Cleveland Mining Heritage Society.
North York Moors Caving Club.