You need an intermediary device.
The foolproof option would be a receiver with a headphone jack. AppleTV HDMI out to Receiver HDMI IN... Receiver HDMI out to TV HDMI IN. This would also give you many other useful capabilities. A good receiver can do many things in an A/V system. It is often considered to be the central hub. While this would certainly work, it would be massive overkill if you have no A/V aspirations beyond this one need.
Option 2 would be a little box designed to separate HDMI audio from HDMI video. Some of those would have a headphone jack and these usually cost a lot less than a Receiver. They are usually called HDMI Splitter or Audio Extractor and similar.
Example
Option 3: if the TV has any kind of audio out, you might find you can get a box to receive audio out from TV and give you a headphone jack. This would be similar to the Audio Extractor just referenced, probably working with the TV's optical out or even RCA jacks. Like this...
Toslink Optical plugs in on the other end (input) and headphone jack plugs into the visible port. Odds are high that this would deliver stereo audio at best.
Option 3B: similarly, if you use a soundbar, it might have some audio out jacks and then a box that can receive from it could give you a headphone jack.
But if you are looking for a
direct way, then NO. AppleTV is throughly locked down. The original generation AppleTV from about 2007 had some analog out options too and Apple has since "improved" on that.
One more thing: presuming you are after wired (superior) quality, so this may not do the job but AppleTV can
connect with Bluetooth speakers including bluetooth headphones. It MIGHT be able to connect with a Bluetooth receiver (
example). So that would be AppleTV wirelessly to Bluetooth Receiver into which you connect your wired Headphones. I'm not sure about this option but it seems plausible to work. Of course, all of the relative negatives of Bluetooth would apply, even if you parked this Receiver right next to the AppleTV.