Hold phone close to the new Apple TV, follow the prompt to sign in and it will automatically download all your apps back. You'll need to sign into your apps manually.
If you have more than one Apple TV associated with the same Apple ID, you can keep the same appearance and apps for each device. This makes it seamless to switch between an Apple TV in the bedroom and one in the living room, for example.
Open Settings
on Apple TV.
Go to Users and Accounts > iCloud and turn on One Home Screen.