How do I approve my new iPhone on another device signed in to iCloud?

What do you mean by “approve”. If you have 2 factor authentication enabled and you log in to your Apple ID on the new phone you should see a notification on the other device if it is signed in to the same Apple ID. It should say that another device is trying to log in. Tap “Allow” and a 6 digit code will be displayed, which you can the enter into the new device.