During the PS4 Pro announcement, it was also announced that PS4 owners would be getting a firmware update that would allow for games to run in HDR quality. Kotaku (Via Game Impress Watch)  reports that it's unclear as to whether or not this update will be free for existing owners. The speculation stems from an interview with Sony executive Masayasu Ito, who stated the decision to charge for the patch to enhance games would depend on the developer...

"It will be different for each title. I believe it will depend on the thinking of each licensee."

Ito then went on to say it will also depend as to whether Sony will charge for the patch with their games as well. It would appear this dispute will only exist for games currently out on the market as all PS4 games from here on out will support PS4 Pro. 

I can't imagine Sony will charge people an individual price per game to play it in HDR quality, but then again I didn't expect the PS4 Pro not to have UHD Blu-Ray. I can say for sure I can live without HDR and won't be purchasing if that's indeed the case. I already bought the game and the console, I don't want to be nickel and dimed.