Microsoft released an update to its Edge beta app on iOS today, which comes through Apple's TestFlight app. The first thing that you're going to see is the new logo, which showed up on the Android beta app yesterday.
There are two other new features, both of which were made available on the Android beta earlier this week. The syncing settings have been changed to let you choose "The new Microsoft Edge" and "Microsoft Edge Legacy". Previously, Edge Chromium was known as Edge Insider, and Edge Spartan was just known as Edge.
The other new feature is a new control center. Tapping on the ellipsis in the center of the navigation bar will show a range of options.
Edge Chromium is set to launch for the desktop on January 15, so it seems likely that that's when these features will come out of beta. That also means that for the first time, you can sync the mobile Edge browser with Windows 7, Windows 8, Windows 8.1, and macOS.
If you want to sign up for Edge Insider for iOS, you can visit this link from your iPhone or iPad.