Family Sharing

I have uncertainty about the process because I have never had to to it, and I have never seen you question answered before. But, here is the process I think you need to follow.

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.

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If this is what you needed to do, then please post back and let me know.

I have read a couple of posts where people were able to delete a chid ID using the steps below.  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