first, at one of the stables, there is a person who gives you a side quest to locate the royal family's (Zelda's) horse on a hill nearby. I forget what the hill is called. If you glide from the nearest mountain, you can easily spot it. But since it has been alone for 100 years, it acts like a normal wild horse. Finally, bring it back to the stable, register it, and you will get it's royal gear