It’s not a federation… do you mean national ones?
Perhaps they will elect a new king next year… or a whole new Royal Family!
Nope. There are no national elections of any kind. The closest thing Saudi Arabia has to a legislature is an advisory council that’s 100% appointed by the King. They only just having local council elections a few years ago and IIRC half the membership of those councils is still appointed by the King (or by the interior minister in his name).