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You can either do this by installing a third-party app like SecureTeen on your child's phone or enable the inbuilt parental controls offered by Instagram.
First, it will be useful for you to familiarize yourself with the information - how to find out who someone is messaging on instagram and start using mSpy to solve this issue. It is one of the best spy apps that offers Instagram tracking function. This feature allows you to track all your Instagram activity. Which happens on the target phone or tablet. Works with both Android and IOS
Modern internet can be dangerous for kids and I think it is good idea that you want to track such activities. I know several bad stories about this and it is really worth attention. But there are a lot of decisions how to protect your kids! I can recommend to read about cocospy application, in my opinion it is really good for such purposes.