Puppet government

A puppet government was a government that exercised little or no real authority, with the real power being held by others. In an alternate timeline, the Daleks created a puppet government on Earth. (TV: Day of the Daleks) The Nimons had a puppet government on Skonnos. (TV: The Horns of Nimon)

Behind the scenes
The depiction of both puppet governments shown in televised Doctor Who are heavily inspired by the "French State" (colloquially known as "Vichy France" or the "Vichy government"), the Nazi collaborationist regime that nominally governed France during World War II.