Dalek Jast was a member of the Cult of Skaro. He and his fellow cultists Sec, Thay and Caan arrived on 21st century Earth via a Void Sphere they used to escape the Last Great Time War between the Daleks and the Time Lords. Jast was tasked with monitoring the status of the Genesis Ark, a Time Lord prison capsule containing millions of captive Daleks.
As the Daleks fought against the Cybermen in The Battle of Canary Wharf, the renegade Time Lord known as the Doctor reversed the polarity of Torchwood's Void rift, sucking in everything saturated with Void particles. The Cult of Skaro survived by using an emergency temporal shift to escape to 1930's New York.
In New York, the Cult conducted their Final Experiment: a procedure that would forcefully bring about the Daleks' evolution and allow them to survive and adapt, saving their race from the brink of extinction. However, after Dalek Sec transformed into a Human-Dalek hybrid and began to exhibit more human behaviour and ideas, Jast, Caan and Thay began to doubt his leadership and declared Sec an enemy after he enlisted the help of the Doctor for the Final Experiment.
When the Cult's army of Dalek-Humans were activated and ordered to find and kill the Doctor, Jast and Thay led them into an empty theater in New York City. The Dalek-Humans disobeyed their Dalek creators since they had been accidentally infused with the Doctor's Time Lord DNA, which disrupted their conditioning. Jast and Thay opened fire on the Dalek-Humans and they fought back, concentrating their weapons fire until Jast and Thay's shells exploded, leaving Dalek Caan back in the laboratory as the last Dalek in existence.