Stalking was the act of following someone in a threatening manner without their consent. It was also a common practice used in tracking prey.
After hearing Tolian Soran speak negatively of time – calling it a predator that stalked one, always killing in the end – Jean-Luc Picard discussed Soran's sentiment with William T. Riker, saying he did not share that view. (Star Trek Generations)
In 2373, Q accused the Female Q of stalking him. (VOY: "The Q and the Grey")
In 2377, Deanna Troi, surprised to meet up with Reginald Barclay at the beach, scolded him for following her on vacation, as she deemed it inappropriate for a therapist's patient to do so. (VOY: "Inside Man")
In 2385, Raffaela Musiker, was court martialed. One of the many charges against her was stalking Vice admiral Kathryn Janeway (PIC: "The Next Generation")