Change my old address to my new address

Billing address or Apple ID email address?

Billing address

You can click the blue Edit payment methods in the article below. When signed in and the page loads, you will be on the credit card page. After updating that, click the Go Back button at the lower left and you will be on the address page.

Apple ID payment information - change.  

Apple ID email address

Note the restrictions in the article.

Apple ID Name Change.        

 What to do after you change your Apple ID or password - Apple Support    I suggest doing this before you change your Apple ID or password.

You can change it in your Apple ID Account https://appleid.apple.com/#!&page=signin