Let's back up here. Why don't you just use your old Apple ID on the new phone? An Apple ID isn't "on" a particular device, it is an account registered with Apple. You can use it on many devices at the same time or sequentially.
Apple ID Frequently Asked Questions - https://appleid.apple.com/faq/#!&page=faq
Just sign in with your old ID on the new phone.
Click on this link to learn how to 'Sign in with your Apple ID' --> https://support.apple.com/HT204053
If another Apple ID is signed in you may need to enter the password for that ID to sign out of that ID first.
Even if you want to continue to use the new Apple ID you will likely need to access the old one to do your cash transfer.
Read how to 'Transfer money in Apple Cash to your bank account or Visa debit card' - (note there is a 1% fee for the instant transfer method but the other method is free)Click here --> https://support.apple.com/HT207882