I just purchased an Iphone 6s plus and it is using IOS 10. There is no Game Center. I have been playing Clash of Clans for years and want to continue on my new phone.
Welcome to iMore! Did you have a back up in iTunes or iCloud? If so, set up or restore with that. If not, download it from the App Store and start over. Game Center is different now. Check with Clash of Clans to see how it is done. It's in the App now. You can challenge friends from in iMessage.