During the Dominion War, the Galaxy saw action in pivotal battles, including the First Battle of Chin'toka in 2374 and the Battle of Cardassia the following year. (DS9: "Tears of the Prophets", "What You Leave Behind")
In 2379, the ship was assigned to Star Fleet Battle Group Omega to engage the Reman Warbird Scimitar; however the Scimitar was destroyed by the USS Enterprise-E before the battle group saw action. (Star Trek Nemesis)
The Galaxy's appearance in "Tears of the Prophets" was confirmed by John Gross and Karen Sickles of Digital Muse in a 25 June 1998 post, by DS9 Visual Effects Supervisor David Stipes, on the newsgroup alt.tv.star-trek.ds9.
According to the Star Trek Encyclopedia (3rd ed., p. 163), as a prototype, the Galaxy had an NX registry prefix much like the USS Excelsior was originally given. However, when the ship made its first on-screen appearance it was given a commissioned NCC registry prefix. This was consistent with the Excelsior, whose NX prefix was replaced with an NCC prefix when it transitioned from an experimental vessel to an operational one.
In an internal list of starships from 26 September 1990, the Galaxy's registry was NCC-59637. It was originally NX-59637.