A Future for our People
Drack gives you the hook for this one in the same conversation which ends his last quest, Krogan Betrayal. Pick up the thread in New Tuchanka on Elaaden, by talking to Hark in the Botany lab (downstairs, but outside).
Hark (probably used to be a herald), relates what happened with the stolen shuttle. Saying you're ready to help will lock you into the mission (it will also bring up the loadout screen, for last-minute re-gearing).
This mission is a lot of short to mid range brawls against Raider types- Cora works well, and if you have biotic charge levelled up, the two of you will go through this place like a pinball machine.
Clear the landing area of some Raider cannon fodder, but check the upper level (north balcony) for a container before proceeding across the walkway northeast.
This triggers a mini-cutscene where it's revealed Spender's man Aroane is here. He runs off, and you gun down everyone who remains.
Drack and Party Member 3 keep talking about crap these Raiders are, and they're not wrong. Storm your way through the base, following the objective marker, and looting containers in your path. As you go, SAM will keep picking up a garbled transmission. This mystery will be resolved when reach the point where you must activate a Lift Rubble cursor to proceed.
Another brief cutscene reveals that the transmitter is Vorn, expert botanist. It looks for a moment like you'll have to choose between saving Vorn or securing the Vault, but it turns out the seeds are useless without this one guy, anyway.
Follow the navpoint to Vorn's hiding place. There's another tete a tete with Aroane along the way, but once more he'll leave his forces to fight you while he retreats.
Kill a few dozen more lackadaisical raiders, then open the Shipping Crate when you reach it.
There's a cut scene here Vorn takes a bullet for Drack (as if a single pistol bullet is going to do a damn thing to a battle-armor'd krogan), and you can choose to support either of them without lasting consequence. When the talking's over, surge ahead into an open area teeming with enemies. You understand cover and flanking about 1,000 times better than they do, so go ahead and wipe them out.
Use the navpoint'd console to take the lift up to the final fight- masses of enemies on the landing platform, backed up by Hydras.
Take them down (the outlying flanges of the platform are very defensible), then join Vorn at console. Using the console will give a moderate AVP award before immediately launching you into a cutscene. The hostage bit resolves itself, but you do have the choice of whether to let Drack murder Aroane. There is (surprise) no lasting consequence for either choice, but if you let him live, his testimony becomes a central part of the case against Spender.
Finishing this dialogue leads to little post-op chatter with Drack back on Elaaden. The conversation ends with Drack's loyalty unlocked, and opens up his Knock 'Em Down epilogue, but the quest itself still has a few more points to hit.
Back on the Nexus, review the Security Footage in Operations to cinch the case against Spender.
Talk to Drack (he's still hanging out in Kesh's office) to launch Spender's downfall.
In the end you'll have to choice to jail or exile him. It's heavily implied that exile is practically a death sentence, given the enemies he's made, but it's also presented as the 'logical' choice. Either way, he ceases to influence the plot, and the mission completes.