In 2370, Commander Donald Kaplan, the ship's chief engineer, regularly engaged in power conversion efficiency contests with Geordi La Forge, chief engineer of the USS Enterprise-D. (TNG: "Force of Nature")
In 2375, Commander Chakotay, under the alias Jason Hayek, infiltrated a Species 8472 terrasphere that was simulating Starfleet Command. Chakotay fabricated a story about just having been transferred from the Intrepid, which according to the story was on a three-year tour of the Romulan Neutral Zone. (VOY: "In the Flesh")
Background information Edit
The Star Trek Encyclopedia (4th ed., vol. 1, p. 374) described the Intrepid as the prototype for the Intrepid-class starship. It was assumed by the authors of this reference work that this was the third Starfleet ship named Intrepid.
A Nebula-class Federation starship Intrepid was briefly considered to be included in an ultimately abandoned TNG Season 6 finale. The vessel was scheduled to undertake a five-to-seven year tour of duty in the Gamma Quadrant. After William T. Riker was given command of the ship, some of its senior officer positions were filled, at his request, by senior officers from the Enterprise. The Intrepid began journeying to the Bajoran wormhole but, en route, the ship was hailed by a Breen delegation and was consequently reassigned by Starfleet to establish diplomatic relations with the Breen. After a Breen science vessel became trapped in an anomaly, the Intrepid was about to attempt a rescue of the trapped craft and Jean-Luc Picard came to visit the Federation starship. Suddenly, however – as the story drew to an end – the Intrepid itself began to be violently pulled into the anomaly, causing a rupture in a transporter room aboard the ship, and Picard, who had been heading back to the Enterprise, was blown out of the rupture. 
The Intrepid was also mentioned in Articles of the Federation.