Instagram not working on Screen time limit

Unfortunately I do not think that is possible at the moment. This could be a possibility in the future.

For the time being the closest option would be to use a screen time passcode. Set a passcode so that only you can change Screen Time settings and allow more time when app limits expire. If you're a parent, use this feature to set up enforceable content, communication, and privacy limitations for your child.

If you're using Family Sharing to manage a child account, follow these steps:

1. Tap Settings > Screen Time.
2. Scroll down and choose your child's name under Family. 
3. Tap Turn on Screen Time, then tap Continue. 
4. Set up Downtime, App Limits, and Content & Privacy with all of the limitations that you want for your child, or tap Not Now. 
5. Tap Use Screen Time Passcode, then enter a passcode when prompted. Re-enter the passcode to confirm. 
6. Enter your Apple ID and password. This can be used to reset your Screen Time passcode if you forget it. 

If you're not using Family Sharing to manage a child account, follow these steps:

1. Make sure that you're on the device used by the child.
2. Tap Settings > Screen Time.
3. Tap Turn on Screen Time, then tap Continue. 
4. Select This is My Child's [device].
5. Set up Downtime, App Limits, and Content & Privacy with all of the limitations that you want for your child, or tap Not Now. 
6. Tap Use Screen Time Passcode, then enter a passcode when prompted. Re-enter the passcode to confirm. 
7. Enter your Apple ID and password. This can be used to reset your Screen Time passcode if you forget it. 

If you would like to request this feature you can submit feedback here:

https://www.apple.com/feedback

If you would like more information on the screen time for IOS you can find it here:

https://support.apple.com/en-us/HT208982