How do I delete an Apple ID and add a new ID?

You can deactivate or delete an Apple ID account. Apple recommends doing the first for the obvious difference noted below.

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.”

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See How to create a new Apple ID https://support.apple.com/en-us/HT204316 and

How to switch Apple IDs on your iPhone or iPad

https://www.imore.com/how-change-apple-id-your-iphone-or-ipad

See the data implications below.

Some of these things may apply even though not changing an Apple ID: What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

 Keep in mind that some things available under a first Apple ID will not be available under a new Apple ID. For example, you won’t be able to transfer anything purchased from the App and iTunes Stores to the new ID. And, there are other issues to be addressed.

And see what Eric Root says on this matter here  https://discussions.apple.com/thread/251483565and

what Winston Churchill says about it here: https://discussions.apple.com/thread/7452747

You also can set up family sharing between the IDs to share purchases made with them. See:

Family Sharing  https://support.apple.com/en-us/HT201060

Set up Family Sharing https://support.apple.com/en-us/HT201088

Do not deactivate or delete the ID before you remove it from your device/computer.