The Ahwahnee, along with thirty-nine other starships, fought the Borg at the Battle of Wolf 359 on stardate 44002. The heavily damaged ship was discovered by the USS Enterprise-D after the battle. (TNG: "The Best of Both Worlds, Part II")
After being salvaged, by early 2368, the Ahwahnee joined Captain Jean-Luc Picard's fleet that blockaded the Klingon-Romulan border during the Klingon Civil War. The ship was one of twenty-three assembled for the fleet and was one of the seventeen chosen for the tachyon network. Identified by its name and registry number, the ship's position in the network was monitored from the Enterprise-D.
When the network was disrupted by a high-energy burst released by the Romulans, the net was no longer effective in a radius of ten million kilometers around the USS Sutherland. Subsequently, Picard ordered the fleet to proceed to Gamma Eridon at maximum warp, where the fleet would attempt to reestablish the net before the Romulans got there. (TNG: "Redemption II" okudagram)
Background information Edit
The Ahwahnee was clasified as a Cheyenne-class starship in an internal list of starships, dated September 26, 1990. It was stated in the list that the ship was destroyed at the Battle of Wolf 359.  However, and despite never having been firmly confirmed as such by production sources, due to the ship having been salvaged and re-used by Starfleet following that battle, the Ahwahnee was presumed by the fanbase to be the sole surviving vessel to emerge from Wolf 359 out of the forty combatant vessels on the Federation side, though the USS Endeavour (NCC-71805) has since then emerged as the more likely contender for that status. (Star Trek Encyclopedia (4th ed., vol. 1, p. 240))
The Star Trek Encyclopedia (3rd ed., p. 470) stated that this starship was lost in battle and named for a Native American tribe. Data's "negative" lifesigns comment in the episode (Act Two, Scene 36), implied that Ahwahnee's crew had been lost as well. The subsequent edition of the Encyclopedia (vol. 2, p. 326) dropped the naming reference, but reworded the "lost" statement as "damaged or destroyed", adding that the wreckage was "later salvaged".
The Ahwahnee's registry number was visible on two different computer displays in "Redemption II", aboard the Enterprise-D and USS Sutherland, where it had the registry NCC-71620. One of the two displays, the Starfleet tactical analysis report, was replaced with a new display for the remastered episode, so that only one display showed the registry.
The original registry NCC-73620, which was also associated with this vessel, was not visible on screen, but could be clearly read off photos of the filming model,  and Encyclopedia author Mike Okuda (whose art department also created the computer displays) actually retconned this one for the fourth edition of the Encyclopedia (vol. 2, p. 326), having used the 71620 one for the previous editions. It is the original registry that became established as the correct one when the ship became featured in 2017 in and on its own, issue 108, outing in the British partwork publication Star Trek: The Official Starships Collection.
Despite the discrepancy regarding the registry numbers, Okuda has always meant the USS Ahwahnee in "Redemption II" to be the same Ahwahnee as seen in "Best of Both Worlds, Part II", as was evidenced in his ship listing that was included in the Star Trek: The Next Generation Writers' Technical Manual, 3rd ed., page 28 (already using the misspelled "NCC-71620" registry), which read, "Damaged by the Borg at Wolf 359."
The aforementioned Ahwahnee studio model, whose name was described by Ed Miarecki,  was a four-nacelled starship built from two scaled-down Galaxy-class model kit saucers, with marker pens glued on as engine nacelles. The model was then painted and damaged before being filmed for "The Best of Both Worlds".