You or the child should sign into the account and make the request. You should have the ID and password from when you first set up the account.
From: How to delete your Apple ID account - How to delete your Apple Account - Apple Support
Section: Can I delete my child’s account?
"Your child can also request deletion of their Apple ID, which requires your approval.
The approval request will be sent via email to the primary Apple ID email address of your family organizer account. When approving the request from this email, you will go through the process of deleting the child account."
If the child's account password is unknown, see the section in this document about using a family Organizer's device to reset the password --> Change your Apple Account password - Apple Support
If you have problems doing that then contact Apple about this request: Click here --> Choose your country or region - Official Apple Support Select your country, then a product and work your way down the menu to the desired issue. If you don't see one then try a different product until you reach a telephone or chat help request and ask to be redirected.
These two posts suggest it may take several weeks for the account to be fully deleted.
- “I spoke to Apple support and it can take up to 30 days to delete the child account [in the system].” - Unable to remove Family Sharing - Apple Community
- “received emails confirming both Apple ID’s had been permanently deleted, and am now able to create a new Apple ID child accounts. The whole process took just over three weeks.”
https://discussions.apple.com/thread/256220811?answerId=261777712022&sortBy=oldest_first#261777712022
