The Royal School is available for purchase at Player L14.
You must complete the Academy of Magic Quest Set in order to make your Royal School fully functional.
Completing "Orders" will cause a "Timed Quest" to appear in your Quest Side Bar - so be sure to check for them quickly, as the timer begins automatically and some have a very short duration!
Completing a Timed Quest gives Colored Runes as Rewards. These do not currently have a purpose but eventually they will act as a form of in-game currency.
Quest Set: Academy of Magic 1-15