Baton Rouge class NCC-1371 was launched in Earth Calender Year 2232 and is now the sole remaining member of the class in service. The Republic has a standard crew compliment of 250 cadets with a further 100 officers and crew. The current Commanding Officer of the Republic is Captain Daniel Walker. The Republic was given all of the latest starship systems and equipment, the latest sensor systems and computers. A refit in 2295 brought the systems of Republic up to date again and she now could not be internally differentiated from newer vessel designs.
The Baton Rouge class starship was the successor to the Daedalus class and was introduced in the 2200s. This starship was fitted out for science and diplomacy with a crew compliment of 344 total. Since taking on the training role the Republic has been upgraded with Achernar sub-class circumferential warp nacelles and technology equivalent to 2280s Starfleet standard. The ship rarely goes to warp drive to save the remaining spaceframe hours and allow the Republic to remain in service for longer. She is dry-docked regularly to service the worn-out frames and upgrade obsolete technology. To allow the technology to fall back too far would be to run out of engineers trained in how to repair them, or spare parts to maintain them with.
The Baton Rouge class has three standard shuttlecraft as well as transporter facilities. The Republic is designed to train Starfleet cadets on starship life and procedures. Missions often take the ship to the outer worlds of the solar system to test the cadets' abilities to perform away team missions and deal with the unexpected under controlled conditions. The Baton Rouge class were capable of over warp eight, but the Republic keeps to warp one or two; this is just enough for the cadets to be familiar with warp drive but not too fast as to wear out her spaceframe. Engineers are concerned now that within the next couple of decades that the Republic will have to be restricted to sub-light travel under impulse only.
U.S.S. Republic is currently engaged in cartographical studies in the far reaches of the Beta Quadrant sections of the Federation. U.S.S. Republic is to enhance and map out these regions using state-of-the-art stellar cartographical technology. Captain Walker is himself an expert in mapping and cartographical techniques, and his skills are most evident on this mission. Since the abolition of the Klingon Neutral Zone, mapping of this area has been opened up more, with more active means of mapping allowable than has been previously the case.
The U.S.S. Republic has been a purpose-converted training ship that has all of the facilities and capabilities both of a state-of-the-art Constitution-class vessel, and of a first-class training facility. Starfleet converted her for use in the role in the late 2240s after the first of the new Constitution class starships came into service. Republic was assigned as a training vessel from 2250 - 55 with the intention of rotating the assignment, but it was decided that the ship would better serve Starfleet Academy by being permanently converted and dedicated to the role. Later, U.S.S. Mars (NCC-525) was also converted from the aging lines of high hull-frame hour Saladin-class vessels, and was retired in 2295.
I took the decision to make the Republic a Baton Rouge class starship, rather than a Constitution, for a variety of reasons. Firstly the ship was a training vessel for Cadet James T. Kirk in the early 2250s, a Constitution class ship would be brand new and not used for a second-rate role like this. Secondly the Republic is NCC-1371, which is a far lower registry number than either Constitution (1700) or Enterprise. Constellation (1017) I can overlook as a production need/anomaly.
The excellent book 'The Autobiography of James T. Kirk' features two Baton Rouge class starships: the Republic and the Hotspur. These are older starships pre-Constitution class starships from around 2200 - 2270 service. Republic is described as being patched up in the novel, but if she is still in service at the time of DS9: The Valiant, then she must have been modernised and repaired to stay relevant.
Designed by Star Trek veteran Rick Sternbach for the 1980 Spaceflight Chronology, the Baton Rouge class was the last starship pre-dlithium and the first with transporters. In the post-Star Trek: Enterprise world, I would assume this design is the gap between the NX-refit design of Doug Drexler and the Daedalus class and the later NX-1700 Constitution of 2245. That would put this as a design from between 2200 and 2210 - a dreadnought era ship compared to the refit Enterprise of the 70s.
Modern real-world equivalents of the Republic are HMS Caroline (the last Jutland survivor in Belfast) and HMS Bristol in Whale Island, Portsmouth: the sole Type 82 destroyer.