Death has many helpers, and this occurs literally. Mortheus, God of Death, has several helpers for his most diverse interests, such as Cayenne and Liktu. The helper who will go after those who try to cheat death is Cayenne.
Cayenne, as well as all of the various servants (those who tried to cheat death) of the God of Death, inhabit the plane of existence called the Mestige. Cayenne, however, was a mortal who charmed Mortheus with her cunning. Hating to cheat death (himself), Mortheus shares his own energy with Cayenne so that she is temporarily and recurrently immortal. In other words, she is not actually immortal, only as long as the God of Death wishes.
The Third Eye is a society of powerful assassins, like Aloy and Nidele, each with unique powers and abilities and Cayenne is an Adept of that group, more specifically their leader. Cayenne gets information from everyone trying to cheat death from Mortheus and communicates it to her group so actions can be taken.
Cayenne is able to communicate telepathically, summon death energy, which kills any living being she touches, teleport, and isolate people in a special dimension where she possesses nearly limitless powers, The Third Eye.
The Adept of the Third Eye will join her assassins for The Tournament of Champions at the behest of Mortheus to prevent any mortal from achieving immortality. Or does she, for all her cunning, have some other interest in this competition?