You can subscribe to Apple Music on your Apple TV.
Apple Music offers a variety of plans including Student, Individual and Family. For more information on each plan, see the Availability of Apple Media Services.
If you join a family group that subscribes to Apple Music or Apple One and you already subscribe, your subscription isn’t renewed on your next billing date; instead, you use the group’s subscription. If you join a family group that doesn’t subscribe, the group uses your subscription.
See the Apple Support article Leave Family Sharing.