I want to delete my old email address. How?

You can deactivate or delete an Apple ID account. Apple recommends doing the first for the obvious difference noted below. But, your circumstances will dictate your choice.

How to deactivate your Apple ID account  https://support.apple.com/en-us/HT208503

“If you request account deactivation, you'll receive a unique alphanumeric access code. When you're ready to reactivate your Apple ID, contact Apple Support, provide your access code, and we’ll help you reactivate your account. If you lose this code, we won't be able to help reactivate your account." 

How to Delete your Apple ID Account https://support.apple.com/en-us/HT208504 

“While your request is being processed, you can contact Apple Support with the unique alphanumeric access code you received, and we’ll help you cancel your request. After your account is deleted, Apple can't cancel the request, reopen your account, or restore your data.”

All purchases made using an Apple ID are tied to the ID. Delete the ID and you will need to download them using your new ID. 

I suggest you do a name change on your existing ID to remove the email account. 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.