Night on the Town
After completing Precious Cargo, you'll get an email from Reyes, asking you to give him a video call. The future is here!
Reyes will invite you as a guest to a party Sloane in throwing in Outcast HQ. You can make it clear you want things to remain professional, or throw yourself at him. If you don't take the latter tack now, you'll still have many, many opportunities later.
Travel to the Outcast HQ on Kadara. Disappointingly, Ryder just shows up in their usual off-duty duds (though, to be fair, so does everyone else). The Pathfinder name cuts no ice with the doorman, but Reyes will show up and escort you in.
You'll chat a bit with the Angaran delegate to Kadara, then Reyes will take off to attend to some business. You're left alone, with a 3-part objective to mingle with the partygoers. The only three that count for the quest are Sloane Kelly (the Outcast boss in the big chair, as you may recall), her lieutenant Kaetus at the door, and then the Angaran Keema Dohrgun again. She has a lot more to say than the others.
There are other, non-quest people to talk to as well. There's the despondent Turian Velus, who screwed up by trying to neg one of the emotionally open Angarans. Tell him to 'Talk to Her' to smooth over their relationship woes.
There's also a gambler in the corner- tell his to pick 'evens' to make his day.
Lastly, Umi is tending bar. She'll make you answer trivia before handing over a drink. The name of her bar is Kraala's Song, and she only serves whiskey neat. Whether you get those questions right or not, you'll still have the chance to try her mix of ryncol & Angaran wine. The combination is... potent.
Whatever your degree of party-rocking, once you've talked to the three marked guests, your objective will shift to tracking down Reyes. Head out through the main door (where Kaetus is standing guard), and then take the first door on your left to find Reyes up to no good.
You'll get in a minor tiff when one of Sloane's guards comes to investigate. Hit the quicktime event to kiss him, or let the moment pass to deck him.
Either way, it works, and you'll escape the party to drink priceless whiskey on a rooftop with Reyes. Even if your flirtation with him to this point has been minor, you'll still have the chance to make this a romantic moment.
The mission completes and you find yourself back on the ground, with the overarching Settling Kadara task set to "ON HOLD - Wait for trouble to come calling." Ominous.