Rigby is correct.
For movies or tv there is no point of 120Hz.
There are literally only 14 movies filmed at a high frame rate (48fps or higher). See the full list of them
here.
Of those 14 movies, only 2 of them are available at a higher frame rate on physical media, and I don't think that number is higher on any streaming platform. This isn't going to change, and higher frame rates are not going to suddenly take off, either. As you can see from the list, filmmakers have been able to film at higher frame rates since the 70s.
You may benefit if there are games you want to play at a higher frame rate, but even then the value you will receive from it remains to be seen. There are currently only 8 titles on PS5 that support 120fps, all of which support it by scaling back on other things like resolution or textures (given PS5 is in its infancy, but you can already see that 120fps is very limited in appeal to developers). There are many more titles on mobile platforms that support 120fps, but again, they make some pretty big sacrifices to achieve it.
Basically, what I'm saying is that your money is better spent going on a tv with other features (like deeper blacks, higher peak brightness or better upscaling). You might spend a lot of money on upgrading your equipment only to find that you get nothing out of it.
To answer your question though, yes, you will need a HDMI 2.1 equipped television that supports 120hz to enable 120hz on the Apple TV.
Edit, just to be clear. Many tvs will claim 120hz panels. That is not the same as having a set capable of taking in a 120hz signal.