After you fight the enemy in Hyrule Castle, new rifts appear, and you learn more about what you must do.
New Features
You can now go into the Equipment menu and switch between the Royal Travel Attire and the Disguise if you wish.
You can also get special outfits when you use amiibo. If you already used three amiibo today, you can now scan another three today.
You can now visit the Hyrule Castle Town shop. They sell a Stone Anklet for 400 rupees. It reduces how much you get knocked back when hit.
You can bind to the bird weathervane and move it. You will reveal stairs beneath it. Go down the stairs and open the chest to get 2 Might Crystals.
You can talk to the kid in the west part of town to start the quest A Curious Child.
At the southern gate of Hyrule Castle Town, you can talk to the guard to start the quest One Soldier Too Many.
Go southeast from the castle until you are between a bridge and a rift to the south. There will be a cutscene. This starts the quest Automaton Engineer Dampé.
Moving On
When you're ready to continue with the story, you can explore the rifts that the king spoke of, by visiting the Lands of the Goddesses.