This MacRumors article, "
How to Use Apple TV's iPhone-Based Color Balance Feature", walks you through the steps to use the new TV color calibration tool that will be available once iOS 14.5 and tvOS 14.5 are released next week.
Note: People who are participating in the beta programs already have access to iOS 14.5RC and tvOS 14.5RC, so there are some who have already tested out this new feature.
Requirements: iOS 14.5 and tvOS 14.5, a 2015 or newer ATV, an iPhone X or later (requires FaceID).
The calibration only works for TV streaming through an ATV. The calibration changes the settings within the ATV so that your ATV will send "your calibrated adjustments" to your TV. Your TV setting will NOT be changed, only thing that changes is what the ATV communicates to your TV. So the calibration changes will only be seen when streaming from the ATV. This will not affect color calibration on other devices or directly on your TV. Also, be aware that the color calibrations will NOT affect, make corrections to, Dolby Vision streams.
I will try this out when the iOS 14.5 and tvOS 14.5 updates are pushed to me in a few days.
The one question I have is about all of my different TV color settings. My new Sony Bravia TV has multiple settings for each connected device. For example, I’ve got the current model ATV 4K (2019?) connected to my TV's HDMI 1 port. For HDMI 1, I have the color options of Vivid, Standard, Cinema, Sport, Gaming, etc. What I don't know yet is whether I only need to select one of those options to perform calibration on, or whether I need to select each one separately and do calibrations. I'm hoping just one, and that the calibration feature will be smart enough to apply the changes for all the others.
I'm also wondering about other settings as my TV can be setup to use various combinations of HDR and SDR. I'm not sure if these settings will affect the calibration.
ETA: Here is a Youtube video on calibrating the color on your TV via new ATV feature.