In 2367, while exploring a cavern on Alpha Onias III, Commander William T. Riker was rendered unconscious by gases. While unconscious, neural scanners scanned Riker's brain. The scanners used elements of Riker's reality and constructed a holodeck simulation with those elements interspersed throughout, so that it felt real to him. What Riker wanted, the scanners made possible.
In one of these simulations, on stardate 49472, Captain Riker, the commanding officer of the USS Titan, was ordered to provide tactical support for Starbase 384, which was located near the Romulan Neutral Zone. In 2383, this starbase was mentioned in Riker's service record that was on display in his quarters on the Enterprise-D. (TNG: "Future Imperfect", okudagram)
This starbase was only mentioned in writing.
This starbase's quadrant of origin is inferred from it being near the Romulan Neutral Zone. This zone was canonically located in the Beta Quadrant in the Star Trek: Picard episode "The Impossible Box".
For the remastered episode of "Future Imperfect", the original text of Riker's service record was replaced.