Apple has today released tvOS 15.1.1 for Apple TV 4K and Apple TV HD.
Outside of the major upgrade each year, tvOS updates are typically minor in scale with a focus on under-the-hood fixes and performance improvements. As Apple does not provide release notes for tvOS updates, we will have to wait and see if tvOS 15.1.1 does include user facing changes. We will update this post if anything of note is discovered.
To install tvOS 15.1.1 on Apple TV 4K or Apple TV HD, go to the Settings channel, then look for the System section near the bottom. From here, look for Software Updates under Maintenance, then select Update Software and Download and Install. Wait for your Apple TV to download the update. Don't disconnect or unplug your Apple TV until the update completes.
More information on how to update the software on your Apple TV is available on this Apple Support page.