Near where the Tempest is moored on the docks of Aya you’ll find an overly curious Angara named Avela Kjar. Indulge her as she asks some questions and she’ll reveal that she’s a bit of a history buff… and she just so happens to need your help digging into the history of her people. On a whim she’s decided you’re good people, and, again, you need to prove yourself a friend of the Angara, a fact she’s willing to exploit to the hilt to get you to work for her. No wonder the Kett attacked these aliens. Anyways, accept her request to go looking for ancient Angara ships on Havarl to start the quest "Recovering the Past".
Fly over to Havarl and from where the Tempest lands head east. Your destination is the large trench that splits the operational area in half. The ancient wreckage is in the middle of the trench, just east of the Forward Station which itself is east of the Pelaav Research Station. Be wary as you approach, however, as the wreck is probably being labored over by some Remnant, not to mention the Remnant, Roekaar and wildlife you’ll have to fight through en route. Destroy any opposition on the way to and around the wreckage, then scan the ship and loot an "Ancient Starship Cockpit" to secure an "Ancient Angaran Pilot’s Helmet".
Return to Avela Kjar in the Repository of History on Aya and she’ll gush about your find before deciding to exploit you further. You have, after all, proved your competence admirably thus far, so she’ll ask you to search for more artifacts on other Angaran worlds, Kadara and Voeld, respectively. This ends the quest "Recovering the Past" and begins "Forgotten History".
Note: If you found the Angaran Artifact on Voeld (during the quest "Uncovering the Past" you’ll automatically hand it over to Avela Kjar during this conversation.