I was born and bred in the north of England and have never heard the surname before. This could possibly be due to the fact that historically Northern England tends to contain more Viking influenced names due to the fact that that part of England was ruled by Vikings for several centuries - and southern England had their own ancient tribal languages plus they had more Norman (French) influences.
However, I do know that "ing" at the end of a word usually means a tract of land and would suggest your surname derived from a farm owned by the "Jest" family. The "s" at the end of the surname could either be plural for more than one tract of land = ings - or in some areas of Britain an "s" at the end of a surname could mean "son of" = Wilkinson or Wilkins.
I was interested to see an online book describing the migration to Nova Scotia and presumably your early ancestors could have been fishermen; or farmhands,; forest workers or miners. If your migrant ancestor fished for a living it would suggest to me that he would have been born and bred near a river or the sea.
A National Archive search only brings up two "Jestings", one having the "Justin" alternative.
At one time, spelling was a bit haphazard and if you search for "Jestings" on
www.familysearch.org Then scroll down and click on the marriage years during the 1700s period, there are about 340 results for the same Jestings, or similar, surname in England. Searching for baptisms over the same period brings over 2000 similar names but very different spelling.
If you know your family followed a naming pattern and the given name you're searching for isn't on the family history website, it might be advantageous to contact the area archives and/or the local family history centre to see if they hold any unpublished church records. There are a couple of reasons for this:-When the Mormans (Church of Latter Day Saints) visited churches in the 1980s to film the books not all churches gave permission and some books were in private hands and eventually donated to the archives..