The authenticator app can be installed on the new phone.
Option 1: When you setup 2FA, take a screenshot of the QR code whenever you setup a new Authenticator for a site and save it in an safe location (eg: Encrypted USB Recovery Key). Should you need to reinstall or add the Authenticator for that site to another phone, simply add the account in Authenticator by scanning the QR code in the screenshot just as if you were setting up a new site.
Option 2: You will need to remove 2FA from your services/exchanges and re-enable by enrolling your new phone with the Authenticator app with 2FA for the site again. You can do this site by site until you’ve restored all your 2FA onto the new phone.