The Supreme Dalek was the leader of the Daleks on Skaro in the Dalek City. He possessed three light bulbs at the dome of its red casing and had a deep voice just like its Supreme lookalike.
He was the Dalek who took the privelege of unleashing "maximum extermination" on Missy and Clara Oswald when they were captured and brought to the Daleks, and ordered for a beamer to destroy the Doctor's TARDIS. (TV: The Magician's Apprentice)
He ordered the extermination of the Twelfth Doctor after he had stolen Davros' wheelchair and mocked the Daleks; however, it failed. He noted how the Doctor was against using weapons only to be scalded by the Doctor, who wanted Clara back. This Dalek proudly professed that Clara was "not alive" angering the Doctor greatly.
He later interrogated Missy, who survived by teleporting at the last second, about Clara's whereabouts, who had also survived. After receiving the Doctor regeneration energy, he praised Davros only to begin to panic about the sudden appearance decaying Daleks coming from the sewers due to them also being restored.
When the Daleks from the sewers began to rise above to the city itself and destroy the Daleks as revenge, he yelled for the Doctor to help them. It is unclear as to whether or not he survived (TV: The Witch's Familiar)
Authority
The Supreme made all the greater decisions involving the Daleks. Unlike his lookalike, he showed respect for Davros, and chose to help him rather than shun him and lock him away by sending other Daleks to assist Davros when he cried for help. He also interrogated and spoke on behalf of the Daleks as well as deciding the fate of their prisoners. (TV: The Magician's Apprentice) He was also keen on exterminating the Doctor, their greatest enemy, quickly ordering his extermination when given the chance. (TV: The Witch's Familiar)