Hello desireé83,
Thank you for reaching out in Apple Support Communities. You can manage your child's contacts by following these steps:
" • Manage a child’s contacts: If you’re using Family Sharing, you can view, edit, add, or delete your child’s
contacts. Tap Manage [child’s name] Contacts.
- If your child already has contacts in iCloud, they receive a notification on their device asking them to approve the request to manage them. If they don’t have contacts, they don’t get a notification and you can immediately add contacts.
- When you manage your child’s contacts, a new row appears beneath Manage [child’s name] Contacts to show how many contacts your child has. Tap the row to view and edit the contacts.
- Allow contact editing: Tap Allow Contact Editing to turn off this option and prevent your child from editing their contacts.
- Turning off contact editing and limiting communication at any time to Contacts Only is a good way to control who your child can communicate with and when they can be contacted."
This will allow the family organizer to manage and prevent a child from adding contacts. These steps are outlined here: Set up Screen Time for a family member on iPhone
Kind regards.