Nothing really, other than being "in spec" as the 1080p spec doesn't include things like Wide Color Gamut. HDR also requires HDMI 2.0a and HDCP 2.2 (sort of, my understanding is that the Dolby Vision type of HDR doesn't). It's all done in software save for a Dolby chip (think betamax vs VCR) offering that all of the MFGs I talked to at CEDIA aren't interested in.
The long and short of it is that there is no incentive to do so. A 1080p TV that they broke all sorts of spec on to make HDR would cost every bit as much, if not more than, a comparable 4K TV. Sales would be dismal, since folks could simply buy a 4K TV for the same price and everyone knows from the constant marketing speech that 4K is better, no matter what size screen.