A monarchy was a form of government with a hereditary ruler in charge.
Earth had many monarchic states. England, (TV: The Day of the Doctor) Scotland, (TV: Tooth and Claw) Great Britain, (TV: The Highlanders) the United Kingdom, (TV: Voyage of the Damned) France, (TV: The Girl in the Fireplace) Spain, (AUDIO: The Marian Conspiracy) Germany, (PROSE: Revenge of the Judoon) Prussia, (PROSE: The Book of the War) Austria, (AUDIO: The Silver Turk) Denmark, (PROSE: The Real Hereward) Sweden, (TV: The Vampires of Venice) Norway, (TV: "The Watcher") Russia, (PROSE: The Adventuress of Henrietta Street) Egypt, (TV: Dinosaurs on a Spaceship) Syria, (TV: The Crusade) Turkey, (AUDIO: Son of the Dragon) China, Mongolia, (TV: Marco Polo) India, (TV: Tooth and Claw) the Roman Empire, (TV: The Romans) the Eastern Roman Empire, (PROSE: Shadowmind) the Holy Roman Empire, (PROSE: The Lonely Computer) Mercia, (PROSE: The Dying Days) the Iceni tribe, (AUDIO: The Wrath of the Iceni) Troy, (TV: The Myth Makers) Palmyra, (PROSE: Combat Magicks) Ur, and Uruk were all monarchies at some point in their histories. (PROSE: Timewyrm: Genesys, Happy Endings)
Though the Draconian Empire was theoretically an absolute monarchy, the emperor still relied on the support of the nobles. It was rare but not unheard of for the nobles to overthrow an unpopular emperor. (PROSE: Doctor Who and the Space War)
Planet Karaoke was ruled by a monarch, whom Clara Oswald accidentally insulted when she attempted to sing in Karaokean without the aid of the TARDIS' translation circuits. (COMIC: The Meddling of Clara's Song)