Almost every realm is a monarchy these days (at least on some islands). But of course, a monarchy can be very much like a republic or a democracy too now since you can customize it in a way you couldn't do before.
Kindara is a Monarchy, though the Ruler is elected monthly and the Judge quarterly. It adds the edge of a Republic without us actually calling it a republic.
Of course, Edmund has always run unopposed, as did Tissaphernes before him, so I'm not sure how well the monthly system is working as intended.