A monarchy can have an elected king. The Resh Galusa was one, so were Polish kings, so is the Pope. You can also have someone filling in for a king (equivalent to the British concepts of a Regent or a Lord Protector).
There are many ways to argue that a frum government needs consent of the governed. A Jewish king could always agree to a constitution with elected representative – and presumably would be bound by his promise (or oath) to respect it.
A Sanhedrin would require all the gedolim to agree (Ashkenazi and Sefardi, Satmar and Lubavitch, Hasidim and Young Israel). When that happens, you’ll know the revolution has arrived.