Puppet monarch

A puppet monarch is a majority figurehead who is installed or patronized by an imperial power to provide the appearance of local authority but to allow political and economic control to remain among the dominating nation. 
A figurehead monarch, as source of legitimacy and possibly divine reign, has been the used form of government in several situations and places of history.
There are two basic forms of using puppets as monarchs (rulers, kings, emperors):
Examples of the first type are the Emperors who were the puppets of the shōguns of Japan and the kings who were the puppets of the Mayor of Palace in the Frankish kingdom. Client kingdoms under the Roman Republic and Roman Empire and the British Empire's colonial relationship with King Farouk of Egypt in the 1950s are examples of the second type.