I don't really know anything about 4k or HDR. So just having an HDR TV won't enhance the movie/ show unless the source has HDR?
Yes, think of HDR as extra information like 4k is, even if your TV is 4k you won't see the benefits of that with a 480p source.
Of course TV's have upscaling options for you to create artificial detail, and most HDR TV's will have a similar mode for HDR that utilizes the expanded capabilities regardless of the source, but you really shouldn't use any of those options as you're not seeing the content properly.
You'll need a UHD blu ray player and a HDR movie to see the real difference, or netflix/amazon have some HDR content, or some new released video games have HDR modes.