Prime Minister of the Daleks

The Prime Minister of the Daleks was the leader of the Parliament of the Daleks of the New Dalek Paradigm. This particular Dalek did not wear any sort of battle armour, but instead situated itself in a clear glass tube. He also spoke with a calm, controlled tone as opposed to the aggressive ranting usually found in Daleks.

Biography
The Prime Minister ordered the abduction of the Eleventh Doctor and his companions, Amy Pond and Rory Williams, summoning them to the Parliament of the Daleks and granting them a mission to lower the indestructible force field of the Dalek Asylum.

Once this had been achieved by the human-turned-Dalek, Oswin Oswald, the Parliament launched an attack to destroy the Asylum. The Prime Minister's memory of the Doctor had been wiped by Oswin, along with the rest of the Daleks. When the Doctor came back to their ship, he was bombarded with "the First Question" ("Doctor Who?") by the Prime Minister and the rest of the Parliament. The Doctor left shortly thereafter. (TV: Asylum of the Daleks)

Behind the scenes
The Prime Minister of the Daleks marks the first time a Kaled mutant has been seen on-screen since the insane Dalek Caan in the Series 4 finale, The Stolen Earth/Journey's End (although an Emperor Dalek with an exposed mutant was seen in the Adventure Game, City of the Daleks).

The same mould used to create the Dalek Caan mutant was used for the Prime Minister.

In The Time of the Doctor, when the aged Doctor goes to confront the Dalek ship, an unidentified Dalek can be heard taunting him. As it is never seen, only heard from the ship, it is unknown if it was the Dalek Prime Minister or another Dalek leader.