Hi. The Gear VR is not compatible with the Note10 series at this time. In a statement made the company addressed this: "The Gear VR is not compatible with Galaxy Note 10 and Note 10+. We remain committed to innovating in VR and AR to deliver incredible new experiences to our consumers."
I can unfortunately confirm what @Leinz and @Rydah have stated, with personal experience. When I got the Note10+ on August 7, and one of the first things I tried was inserting it into my Gear VR (latest model), and while it did fit (barely), nothing happened. It didn't react to the Gear VR at all. I later started seeing statements that Gear VR will not be supported. So at this time I have no idea if a new Gear VR model will be coming out at some point in the future, or if we're done with it. From what I read, Google Daydream doesn't work with Note10+ as well.