The Phoenix Cluster was a stellar cluster.
In 2368, the USS Enterprise-D became the first Federation starship to visit the Phoenix Cluster, on a two-week survey mission. Prior to the mission, several scientists transferred aboard the Enterprise from the USS Zhukov to assist. The mission was interrupted by the proliferation of a Ktarian game on board, part of a Ktarian plot to take over Starfleet. (TNG: "The Game")
According to the Star Trek Encyclopedia, 4th ed., vol. 2, p. 139, this stellar cluster was "in part, named for the Phoenix Asteroids in John Carpenter and Dan O'Bannon's film Dark Star."