Could someone tell me how to approve a new phone?

Do you mean linking your new phone to an existing Apple ID? If so, follow the instructions here: Sign in with your Apple ID - Apple Support

1. 1. Go to Settings.
   2. Tap Sign in to your [device].
   3. Enter your Apple ID and password.
   4. If you protect your account with two-factor authentication, enter the six-digit verification code and complete sign in.

If you are asking about how to set up two-factor authentication, follow the instructions here: Two-factor authentication for Apple ID - Apple Support

1. 1. Go to Settings > [your name] > Password & Security. 
   2. Tap Turn On Two-Factor Authentication.
   3. Tap Continue.

Hope that helps.

Patricia