In 2151, the Earth ship Enterprise made first contact with the Axanarri under unfortunate circumstances. An Axanar vessel was found adrift in space, with its crew hooked up to draining tubes The Axanarri were being harvested for their triglobulin. In the aftermath of that incident, the Enterprise visited Axanar. (ENT: "Fight or Flight")
In early 2251, Captain Garth of Izar won a major victory against the Klingon Empire at the Battle of Axanar. Following the battle, the USS Republic, under the command of Captain Rollin Bannock was dispatched on the Axanar Peace Mission to maintain peaceful relations with the Axanarri. The mission was successful, and many participants received the Palm Leaf of Axanar. (TOS: "Whom Gods Destroy", novel: My Brother's Keeper: Republic).
The Larson-class destroyer USS Axanar (NCC-4448) of the early to mid-23rd century was named after the planet, as was the Normandy-class supercarrier (registry NCC-36003) of the 2310s. (Starfleet Data File: "Starships of the Fleet, by Registry/NCC Number", stardate 11201 revision)