The Ahwahnee, along with 39 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 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 registry number was visible on two different computer displays in "Redemption II", aboard the USS Enterprise-D and USS Sutherland, where it was given 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 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.
Despite the discrepancy regarding the registry numbers, Michael Okuda 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".