A monarchy was a form of government with a hereditary ruler in charge.
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)
Aneth was the home planet of the Anethans and was ruled by a monarchy. (TV: The Horns of Nimon)
Traken once had a monarchic system of government. (PROSE: The Immortals)
The planet Eros had a monarchy when the Eighth Doctor and Samantha Jones visited it. (PROSE: The Queen of Eros)
Circa the 26th century, the Folflower system was a constitutional monarchy, based on Folflower. (PROSE: The Graves of Mordane)
Gavin was the heir to the monarchy of a planet halfway across the universe without knowing it. (TV: The Empty Planet)