An interesting example of this is Indira Gandhi, who was the prime minister of India.

After the second Prime minister of India, Lal Bahadur Shastri passed away in 1966, the leaders of the ruling party, put her in power as the prime minister, believing that they could control her from the background. One of them famously called her 'Gungi Gudiya' i.e Dumb Doll.

She went on to first split the ruling party, and then after winning the 1971 war, went on to win the parliamentary elections with a landside; After that she was responsible for setting up of the emergency for a short period, where most civil liberties were suspended. She lost the election after that, only to come back in the next elections, and was prime minister till her death in 1984

Sources: Indira: The Life of Indira Nehru Gandhi -Katherine Frank

Edward III of England had little power at the beginning of his reign with his mother Isabella and her lover Roger Mortimer (who deposed his father) being de facto rulers, executing some of the opposition with little or no input from Edward - including his half brother Edmund. A little before his eighteenth birthday Edward seemed to have grown tired of this and had his companions seize Roger and his mother and had Mortimer tried for crimes such as "Assuming Royal Power" then had Mortimer hanged while his mother was effectively placed under house arrest for the rest of her life.

Source: The Plantagenets, The Kings Who Made England - Dan Jones

Adolf Hitler had originally been made chancelor of Germany as a final desperate attempt to keep the country from descending into open civil war. The people around imperial president Hindenburg thought they could control Hitler, who was seen as deranged but also politically unskilled. They had each attempted to lead the country as imperial chancelor but all had failed to find a legislative majority. Hitler was the figurehead of the right wing and had refused to participate in any coalition that didn't feature him as the top dog. So with no other option than either making Hitler head of government or seeing the country possibly turning into the Soviet Republic of Germany, they tapped him for the job.

Not long after Hitler's inauguration as imperial chancelor, a communist terrorist allegedly set the parliament building on fire. Hitler seized the moment to have a law enacted empowering him to do more or less as he wished from then on, marginalising Hindenburg and his advisors with him. (I wrote "allegedly" because to this day it isn't really settled whether it was all a false flag operation by the Nazis or not.)