There is no ice rink or royal promenade. Some things had go in order to accommodate the new venues according to CEO Adam Goldstein. However the ship will have something similar to the promenade which they'll reveal at some point down the road as we wait 18 months to actually see the ship.
I'm going to go out on a limb and predict that at some point RCI starts refurbishing the ships with ice rinks and removing them, making it into a different venue - perhaps turning them into the SeaPlex with bumper cars and so forth. The rinks suffer from the same problem as the main theaters - they are closed most of the time and you have large spaces sitting there empty, or just being used for rehearsals and the occasional ice skating lessons/open skating. Plus I personally feel the ice skating is passť.
As they did with the Oasis class, the suits at RCI will see which new Quantum venues are a hit and look at adding them to older ships as they did with the Royal Advantage enhancements.