In 2269, the USS Enterprise received signals from Questar M-17, a hypergravity object that was probably a neutron star. They discovered an alien ship of great age in orbit about the object, and aboard that ship, a malevolent alien entity that quickly infiltrated every ship system. They were able to escape the entity by tricking it into believing they intended to ram their ship into the star, but seconds after the alien fled, they managed a slingshot, leaving the alien trapped within the star's gravity. (TAS: "Beyond the Farthest Star")
Neutron stars also featured in the Star Trek: Voyager novel Death of a Neutron Star, where USS Voyager discovered a dying dinary neutron star system that was destined to turn into a supernova that would carve a mass of destruction through the Delta and Alpha Quadrants. With the aid of two alien visitors, the crew were able to thwart a plot to use the star as a weapon, and subsequently stole an alien ship to trigger the binary's death early and send the star on a path that would do no damage.
In the Star Trek: The Next Generation novel Dyson Sphere, a neutron star is used as a weapon. One end of an artificial wormhole is opened near a black hole where neutron stars are spiraling in at one-third warp. the other end opens and the star is on course to strike a Dyson sphere. Just who did this is unknown, although the Borg are suspected.