Your highness! Anything royal has to do with a king or queen. The official announcement a queen makes is a royal declaration. Unofficially, royal can mean fit for a king or queen, like a royal welcome with cake and balloons.
Queen Elizabeth's corgis could be called the royal dogs, and the people who work at Buckingham Palace are the royal staff. Queen Elizabeth herself is royal — when royal describes a person it means someone who's a queen or king or belongs to a monarch's family. You can also use it sarcastically by saying someone’s a royal pain. No royalty necessary.