The Turian Ark
You’ll first hear of the Turian Ark once you land on Havarl, which you gain access to after completing the story mission A Better Beginning.
SAM will make note of an encampment of Turians on the planet, which begins the mission Turian Ark: Not Dead Yet. Follow the waypoint over there and help them out with some attacking Angarian Outlaws.
Here you will meet a Turian officer named Avitus Rix, who crash landed out of the Ark some time ago but cannot remember much else. He is on the hunt for the Ark too, so agree with him to split up your search efforts, at which point the mission will be put on hold.
After you’ve progressed through the story some more, you'll have access to the planet Eladaan. Check your emails and Rix should have contacted you with more news of the Ark’s location, which initiates the mission Turian Ark: Lost But Not Forgotten.
Get to the waypoint and you’ll discover a bunch of destroyed Cryo Pods, so head back to the Tempest and inform Rix, who will enlighten you on another possible location for the Ark.
Follow Rix’s navpoint coordinates to find to the abandoned Ark, which you must board and investigate to figure out what happened. There’ll be no enemies here, so just follow the directions until you reach the SAM node, who will inform you about the Ark’s fate.
After you’ve learned about what happened, and appointed Rix as the new pathfinder, the mystery of the Turian ark has been officially solved.