The New Time Lord Empire was an empire created by the Master and the Toclafane during the Year That Never Was. The Master quoted his dominion as "the new Time Lord Empire" as Gallifrey had previously held an Empire in the time of the Pythia. (PROSE: Cat's Cradle: Time's Crucible)
The empire was established on Earth by the Master, who used a paradox machine to allow an army of altered humans, now known as Toclafane, into the 21st century from Utopia, in the year 100,000,000,000,000. Upon entering the year 2008, the Toclafane killed one tenth of the human population and imposed martial law over the planet, causing other races to avoid Earth as the planet was entering terminal extinction.
During his first year as ruler of Earth, the Master forced the human race to build rockets that would carry the Toclafane army into the stars to conquer the universe for the empire that would last till their home time. The fleet of two hundred thousand ships would launch on the anniversary of the day he took power.
The empire fell after Martha Jones travelled the Earth, spreading the Tenth Doctor's name. At the moment the rockets launched, everyone on Earth thought of the Doctor and, having become linked through the Archangel Network, were able to free the Doctor and return him to his normal state. Jack Harkness destroyed the paradox machine, sending the Toclafane to their home time and reversing time on Earth to before the Toclafane invasion. (TV: The Sound of Drums / Last of the Time Lords)