Much like its predecessors, Mass Effect: Andromeda allows you to gain the trust and respect of your relatively untested team by completing loyalty missions for them. Some, like Drack's, just help to flesh out the characters a little more. PeeBee's will unlock a secret tech skill for you.
Cora Harper's (your dad's second-in-command and former Asari Commando) is a little different: She wants you to find the Asari Ark, which was lost in transit upon entering the Andromeda system.
Since Director Tann and the rest of the Nexus are also interested in finding the Ark, it's worth your while to seek it out. Here's how you do it.
Mass Effect: Andromeda Asari Ark: how to complete "Cora Harper: Asari Ark"
Once you've completed "A Better Beginning," the game's first Priority Op, on Eos and have traveled to either Havarl or Voeld as part of the main quest, you should get an email from Cora. According to IGN, she'll say she's found some information about the Asari Ark in Podromos, your outpost on Eos, and she'd like to go with you to follow up on it.
Once you touch down at Podromos, you'll want to follow the nav point to an Asari named Hydaria, who will tell you that kett attacked the Asari Ark and that an evacuation followed. She tells you that if you find the transponder from one of the evac ships, the Periphona, it could lead you to the Ark.
Unfortunately, the transponder is somewhere on Voeld.
Once you get to Voeld, hop in the Nomad and head for the nav point marked on your map. It'll be a false positive, and SAM will say the signal might be bouncing off the ice on Voeld. At this point, several other nav points will pop up. Normally, you'd have to scan all of them, but we're just going to tell you that the one you're looking for is the farthest to the east on Voeld's map.
Once you get there, prepare for a fight: The kett got here first, so you'll have to clear them out to make sure they don't find the Asari Ark before you do. Once you've taken care of them, scan the transponder and then interact with it. Cora says she'll be able to use the flight data on the transponder to triangulate the position of the Ark, but it'll take some time. That's about all you can do with it at the moment, so you'll have to play through the Priority Ops some more in order to find the Ark proper.
Mass Effect: Andromeda Asari Ark: how to complete "Cora Harper: At Duty's Edge" and find the Asari Ark
You won't find any new leads on the Asari Ark until after you've completed "A Trail of Hope," according to Twinfinite, so you've got some time.
Once that's done, expect another email from Cora. She's managed to get coordinates off the Periphona's transponder, and they're pointing in the direction of the Valay System (which you conveniently opened as part of "A Trail of Hope"). If you head to the Valay System, Suvi will alert you to an anomaly — use your scanner and probe to find it and wouldn't you know it? It's the Asari Ark.
You'll then have the opportunity to board the Ark and head to the bridge, where the captain and the current Pathfinder, Sarissa Theris, will enlist your help. You'll have to restore the ship's power so it can make a faster-than-light jump out of the Scourge and onto the Nexus.
Unfortunately, the systems you need to reboot are in areas lousy with kett boarders, but it's nothing you, Cora and whoever else you bring along (we recommend PeeBee for maximum Asari viewpoints) can handle.
From there, you'll head to the hangar, where you'll meet a young Asari commando named Vederia, who will offer to help you. She'll lead you through the Ark while you fight off waves of kett, and eventually you'll reach a Mass Effect Generator that's draining power from the Ark and preventing its escape.
When you go to disable it, you'll find out something... unfortunate about Sarissa. We won't spoil it here, but it's bad. Bad enough that it makes Cora angry, and she totally idolized Sarissa beforehand.
While trying to deactivate the device, you'll be thrown into a couple fire fights with the kett, and the final wave will pit you against a kett Valiant, which plays out like the kett Cardinal from the Trail of Hope mission on Voeld.
Once you've done that, head back to the bridge to confront Sarissa and make some decisions that will likely have consequences down the road. Regardless of what you decide to do with Sarissa, the Asari Ark is safe and you've taken a huge weight off Cora's mind.
More Mass Effect: Andromeda news, updates, tips and tricks
For more on everyone's favorite space opera, check out the rest of what Mic has to offer. Here's an essay on the troubling history of colonialism in Mass Effect, a story about the horrifying harassment campaign carried out against a former BioWare employee, a guide to removing Ryder's helmet, a guide on romancing Keri, a guide to romancing Reyes and a quick explainer on the different types of health in Andromeda.