Eye of Cat - Roger Zelazny

William Blackhorse Singer, the last Navajo on a future Earth, is called upon to aid in protecting an alien diplomat from a powerful and hostile member of his own species. With the aid of a shape-shifting alien known as "Cat," he carries out the mission, with one condition: when the mission is over, Cat wants a return bout with the man who captured him, a chase with Singer as the hunted instead of the hunter . . .
Eye of Cat takes a twist on the hunter turned hunted. William Blackhorse Singer is hired to protect an alien diplomat, then enlists the assistance of a shapeshifter he captured years earlier. The creature will only help on the condition that it gets a chance to try to trap Singer once the mission is completed.