Welcome to our Forum, flycat.
When you go back to the main menu, you'll be able to choose a new aspect. When it starts, your priest will be the new Monarch of a brand new (and empty) kingdom. You can play as many kingdoms as you want, but you'll probably get bored because each one will have to start with the beginning ambition. It will probably be more interesting to just continue playing through the ambitions. And, no, your kingdoms cannot trade with each other.