This quest starts after you complete the quest "Recovering the Past" on Havarl. There are multiple parts to this quest, requiring you to dig up three Angaran Artifacts, one on Voeld (see the quest "Uncovering the Past") another on Kadara, and the final one on Elaaden. To get the Angaran Artifact on Voeld you must complete the quest progress required for "Uncovering the Past", which may be quite a bit of work. There’s no good reason to not grab the Voeld artifact during that quest, so it will be presumed you did so for the purposes of this guide.
The artifact on Kadara, on the other hand is right out in the open. Just takes a bit of driving and mountain-climbing to get. From the wind farm drive northwest until you reach a fork in the road near some Remnant ruins, at which turn northeast until you find another fork. At this second fork turn northwest again and follow the mountain road along its narrow confines. The road will eventually lead to - and terminate at - the more open northwestern corner of the map, named "Kurinth’s Valley".
North of where the road ends is a toxic lake. The area you’re looking for is on top of the mountains to the northwest of this lake, over some hills that obstruct your view. These mountains are also southeast of the structure the two stoned Outlaws reside in (see the quest "Emergency S.O.S."). Despite their proximity, you’ll want to approach from the east… or south, or west. Any direction but the north, really, as the slope from these directions is less steep.
You should have no trouble running and jumping your way up to the navpoint on the top of this mountain, where you’ll find a ruined Angaran shrine. Simply grab the Angaran Artifact off the ground when you get here, an "Ancient Angaran Musical Instrument" to be more precise. Before you leave, loot a container nearby, then head down the slope to the west, northwest, as there’s more plunder to be had down there. It’s also worth noting that the ruined structure down here seems to be a mix of Angaran and… Remnant? Weird.
Return to Aya and find Avela Kjar in the Repository of History, where she eagerly awaits your return with some Angaran Artifacts. Having obtained the relics on Voeld and Kadara, talk to Avela (multiple times, if necessary) and she’ll comment on the items as she receives them. Afterwards, this quest will go dormant.