The .Hospital new TLD will be available for everyone to register this March 22, 2017. Still at Early Access Program (EAP) for the next two days, meaning you can register a domain name using .Hospital extension in advance. Of course with extra fee.
I checked KING.hospital at NeedName.com Domain Name Registration Service. I can register the domain via EAP for $197 with a renewal of $59.99. With this information, I assume the registration fee is $59.99 per year on general availability.
For obvious reason, the registry main target are Hospitals. The question is will they be willing to change their website URL address that they use for many years to something .Hospital? Only time will tell.