Some key Instagram privacy settings that parents and carers can use on their child’s account include:

Comment controls - You can block comments from specific people, hide ‘offensive’ comments, limit comments to followers, and filter certain words and phrases.

Resharing to stories - You can control whether or not other people can reshare your posts.

Photos and videos - You can prevent people from automatically adding pictures of you to your profile without your approval and hide photos and videos so they don't show in your feed.
Mentions - You can control wether other users are able to mention you in comments
Story - You can hide your story from certain users and control who is able to reply to and share your story.