In the 2250s, Aerfen was part of a task force assigned to protect Federation colony worlds along the Klingon Empire's border with the Federation. One of Aerfen's many ports of call was Ganjitsu, where a young Hikaru Sulu once snuck aboard the vessel. While Sulu hoped to make an attempt to sign up as a crewmember, Captain Hunter gave him a guided tour and then left Sulu behind as the ship left port.
In 2264, Sulu was expecting to be assigned to the Aerfen after completing a training tour at Starfleet Academy, but was surprised to find himself transferred to the USS Enterprise. (TOS novels: Enterprise: The First Adventure, The Entropy Effect)
In 2270, the Aerfen was in orbit of Aleph Prime mining colony for a port call after being damaged by Klingon Neutral Zone border skrimish action. The Aerfen returned to lead squadrons on patrol along the Klingon border, and was planned to rendezvous with the Enterprise there. (TOS novel: The Entropy Effect)
In an alternate timeline, Aerfen similarly visited Aleph Prime. While in the Aleph star system, Aerfen contacted the Enterprise, which had been called by an ultimate code distress call. Although the Enterprise initially maintained procedural communication silence, after Captain James T. Kirk discovered the ultimate signal had been falsified, he initiated contact. The communication allowed Kirk to converse with Hunter, an old companion of his from his Starfleet Academy days. The contact between the two vessels also gave Sulu a chance to marvel at the vessel he had toured years before, and had hoped very much to serve aboard.
With the Enterprise taking responsibiliy for a prisoner, the apparently murderous scientist Georges Mordreaux, the ships parted ways as Enterprise left for a slow cruise to an Aleph syastem rehabilitation colony and the Aerfen departed for the Klingon border. Because of the old associations awakened by the meeting, Sulu requested a transfer to Aerfen, as he felt his career on Enterprise was in danger of growing stagnant. Kirk also was struck by the encounter, and wished to reassociate his relationship with Hunter. The crew of Aerfen was stunned to hear of the sudden murders of Kirk and Sulu's lover, Mandala Flynn, and the poisoning of another crewmember by the criminal Mordreaux. Aerfen returned to Enterprise's vicinity to provide support for the vessel, and found that many aboard were behaving erratically after Kirk's death, including Mordreaux (who paradoxically never left his quarters during the time of the murders) and Spock, who was unable to account for his whereabouts after the murders. The Aerfen investigation continued to close in on Spock and Mordreaux, who were time travelling using the physicist's new method of time warp.
This timeline was averted, when Spock traveled back in time and aborted the initial use of the time machine which caused the later events to no longer have happened. The falsified distress call was never sent, and Mordreaux was never driven to insanity by the time travel process, meaning that none of his victims were ever murdered. (TOS novel: The Entropy Effect)