Thirst was the feeling of needing to drink fluids to stay hydrated. The word could also describe any intense longing for something.
In 2269, when asked by Rayna Kapec about what loneliness was, Flint answered in metaphors, saying, "It is thirst. It is a flower dying in the desert." (TOS: "Requiem for Methuselah")
A person or species who took pleasure in violence and murder could be said to be bloodthirsty. (TOS: "Who Mourns for Adonais?"