Can I get Center Ice or NSG on my Apple TV

The NHL app should give access to NHL Center Ice, with your tv (cable) provider login credentials, if they carry NHL Center Ice in your subscription package. NHL.com | Subscribe | Support | FAQ | How do I access NHL.TV using my NHL Center Ice subscription?

MSG GO doesn’t list Apple TV, but it is available for mobile (iPhone/iPad/iPod Touch). So AirPlay might be an option? Like the previous, it requires a subscription to a tv provider with MSG Networks in their package.

if it's the newer 4g or 4k models you can get any source that the content providers make apps for and add to app store

if the older models then they are no longer being updated server side which is the only way content is added