How to delete Apple ID

If you are talking about a child in the context of Family Sharing, see Family Privacy Disclosure for Children https://www.apple.com/legal/privacy/en-ww/parent-disclosure/. Toward the end of this document you see: this heading Access, Correction and Deletion. Here is a quote from it.

"If at any time you want to access, correct or delete data associated with Family Sharing or your child's Apple ID, please contact us here: www.apple.com/privacy/contact/."

Using the above link, here is where to pursue you deletion of a child's Apple ID: Privacy Inquiries https://www.apple.com/privacy/contact/. Fill out the form provided on this link.

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 you sign out from the places in the 4th link before deleting the ID.

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