If you've configured your clusters to use a private registry, you can still use Config Sync to manage your configurations and policies. Config Sync automatically detects when a private registry has been configured, and ensures that it's used. However, each version of Config Sync requires a specific set of versioned images to run. If you're using a private registry, you need to push versioned images to the private registry before you can install or upgrade Config Sync.
For more information about using Config Sync with a private registry, see Update Config Sync using a private registry in the Config Sync documentation.