The Outer Rim was an area of space that is distant from Federation core worlds.
Captain Clark Terrell had never visited the Outer Rim before his mission to Te Awamutu VII in 2282. (ST - Alien Spotlight comic: "Alien Spotlight: The Gorn")
In 2364 the USS Enterprise-D visited the region, and while there the Enterprise crew had little contact with Starfleet Command. (TNG episode: "Conspiracy")