Other forms: regalities
The word regality is used for the state of being a monarch — or resembling one. The regality of your queenly cat, calmly looking down on the chaos of your new puppy, is indisputable.
Long ago, it was common to use the word regality to describe the position of being a queen or king: "Elizabeth II entered the regality in 1952." These days, it's more commonly used in a figurative way, for things or people that resemble royalty. If you're staying at a magnificent castle for the weekend, you might walk in and observe, "Wow, this place is full of regality!"