The Ajax was one of the ships that received Kosinski's experimental warp drive upgrades in 2364. The engineering staff reported a measurable increase in performance and engine efficiency following the upgrade. It was later suggested that these enhancements in performance may have been attributed to straightening out simple engine inefficiencies experienced by the older ship. (TNG: "Where No One Has Gone Before")
In 2367, the Ajax was on a deep space exploration mission in Sector 21834. The ship was named on the chart "Starfleet Operations-Sectors 21166-23079" on the USS Enterprise-D bridge. (TNG: "Brothers" okudagram)
In 2368, the Ajax was assigned to Captain Picard's fleet that blockaded the Klingon-Romulan border during the Klingon Civil War. It served as a focal point in the tachyon detection grid, as it was linked to thirteen other starships during the grid's initial deployment. The location of the ship in the grid was labeled with the ship's name and registry. (TNG: "Redemption II" okudagram)
In 2369, the Ajax was on a deep space exploration mission in Sector 21396. The ship was named on the chart "Starfleet Operations-Sectors 21538-23079" in the Enterprise-D observation lounge. (TNG: "Chain of Command, Part I" okudagram)
In the episode "Brothers", the Ajax was identified as an Excelsior-class starship with the registry of NCC-13554.
In Star Trek: Legacy, Ajax appeared as a playable starship, designated as a scout.