In a post from 2012 entitled Changing Guisborough market day: 1813, there is a picture of the priory and this is a message to Ben G, who asked in a comment if I had any information on that picture.
I can't reply direct because messages that come to me from a comment don't have the writer's email! I need a message to my email via the Contact Me section for that.
The answer, hoping that Ben finds this, is that it's a photograph of an old picture that I inherited and so I'm afraid I don't have any information. Check one of the 19th century local histories and see if it's there? Perhaps the Rev Graves' history?