Restrict Game Centre
Restrict Game Center
To restrict Game Center features:
- Go to Settings and tap Screen Time.
- Tap Content & Privacy Restrictions, then tap Content Restrictions.
- Scroll down to Game Center, then choose your settings.
You can restrict these Game Center features:
- Multiplayer Games: Prevent the ability to play multiplayer games
- Adding Friends: Prevent the ability to add friends to Game Center
- Screen Recording: Prevent the ability to capture the screen and sound
Taken from Apple's Support Page.