As above, just plug it in - but you may need (or rather, want, for best experience) to use the correct HDMI input on your TV (be sure to use one that has the most recent HDMI standard/higher refresh rate for 4k/HDR/etc.) and it may pay to go through your AppleTV settings afterwards to re-detect/re-enable the 4k related features for your new TV.
But outside of that you should be able to "just plug it in and it should work".