On the Ismay ONS website it says is the citation that it was from FamilySearch's film 207622 ("Index to probate records, Newcastle-upon-Tyne"). It is not clear in the catalogue exactly what is found on that film:
https://www.familysearch.org/en/search/catalog/results?q.filmNumber=207622
It might just not have been proved, so not found with the usual probate court records. You might need to access the film (or find someone who could do a lookup) at a Family History Center to find out.
It does say that the records filmed were from City Archives, Newcastle-upon-Tyne. Might be worth an email to Tyne & Wear Archives to see if they can help track it down.
That was a good spot by Alexander about that number being an LDS film number given in the original post link. Shame it is locked online on the LDS Search under Catalogue on their drop down menu.
This is partly in the reply by Alexander above:-
Index to Probate Records, Newcastle upon Tyne. Church of England. Parish Church of Newcastle-upon-Tyne.
Secondly, also coming up for that film number is the:-
Index to the Sessions Order Books of the Newcastle Quarter Sessions.
So as well as the Probate Court the Will
may have been an exhibit or used in a Court case (separate to the Newcastle Probate Court)?
Some strict Dissenters' and other non CofE would
not accept the jurisdiction of the Church of England and
some would not have their children baptised by the Church of England either.
I came across a 19th Century Dissenters' case in the newspaper who were being taken to Court by the Parish Church for non-payment of the local church rate.
They would pay the Poor Rate, but refused to pay the church rate.
Mark