Stenza

The Stenza were a warrior race and the self-proclaimed conquerors of the Nine Systems.

Biology
Relative to Earth, they had cold skin and could kill humans by placing their hands to the face and freezing them to death.

Culture
They would then take a tooth from their victims as a trophy, and graft it onto their faces. According to the Thirteenth Doctor's analysis of one of their transport pods, they came from 5,000 galaxies away from Earth and the Milky Way. (TV: The Woman Who Fell to Earth)

History
They conquered and terrorised several planets in the Twelve Galaxies, including Albar and Desolation, forcing the residents to create weapons for them to use. These included bioengineered species, such as the sentient, murderous Remnants, and flesh-eating microbes in the water. These weapons (living and otherwise) eventually destroyed all life on Desolation, save for the microbes themselves. (TV: The Ghost Monument)

In order to decide who would become the next leader of the Stenza, an individual would be given a randomly-selected "trophy" to hunt and capture without the use of weapons or assistance. One Stenza called Tzim-Sha travelled to Earth in his pod in order to capture his selected trophy, Karl Wright, so he could become the leader of the Stenza, but cheated by using a Gathering Coil to locate him. (TV: The Woman Who Fell to Earth)

Behind the scenes

 * T’zim-Sha's character profile on the official BBC Doctor Who website, a non-narrative source, names the Stenza's hunt "The Ritual of the Stenza". These exact words were actually used by Tzim-Sha in The Woman Who Fell to Earth.
 * Stenza are similar to the aliens from the Predator franchise, as they are warriors who hunt for trophies and take a part of their target as a trophy.