How do I get rid of an old Apple ID account

If you want to cancel your Apple ID account, you can deactivate it or delete it.

Apple ID - How to deactivate your Apple ID account.    *

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. There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID.  Make sure that you sign out of all your devices to avoid issues with apps that use your Apple ID account or iCloud. After your account is deleted, you can't sign out of iCloud or turn off Find My iPhone Activation Lock on your devices. If you forget to sign out, you might not be able to use your device when your account is deleted.

How to delete your Apple ID account.   *  

Apple ID – How to Delete.  -

Delete Apple ID (new).   -

What to do after you change your Apple ID or password - Apple Support   -