Unfortunately, to take advantage of HDR on the Xbox One S, you'll need a TV that supports HDR.
And not just any HDR TV will do, as the Xbox One S supports a specific standard of HDR called "HDR 10." If your TV only supports the other standard, called Dolby Vision, then you might not be so lucky. It's like the HD DVD vs. Blu-Ray battle all over again.
So, if you've bought or plan to buy an Xbox One S, and you're considering upgrading to an HDR TV, make sure it supports HDR 10.
You'll also find that most TVs that support HDR these days will also support 4K resolution. That works out nicely with the Xbox One S' 4K video support for playing 4K videos. But again, keep in mind the Xbox One S doesn't play games in 4K. Instead, it'll upscale 1080p games to 4K, which often looks better than 1080p, but not quite as good as native 4K. Trusted Reviews reviewed the Xbox One S and concluded that it's "good at upscaling games."
If you were hoping the Xbox One could play games in 4K, you might want to wait until next year. Microsoft is planning to release another version of the Xbox One currently called "Project Scorpio," which will have all the power needs to support 4K as well as virtual reality headsets and Microsoft's augmented reality headset HoloLens.