Before you run off to tackle any of the new quests that have popped up around Heleus Cluster (save for the "obligatory" Movie Night preparations for Jaal), you might as well return to the Nexus. You'll find more quests there, for one, but you'll also get some story-based events out of the way and make some steps towards Meridian.
Travel back to the Nexus, where Taan will take obvious delight in welcoming Ark Paarchero to the Nexus. Listen to his speech, say a few words of your own, then endure some thanks from some Salarians. Afterwards you'll be free to explore around - your next task is to meet the leaders of the Initiative in Operations. Fair enough, that's where most everything else of interest is.
Task - Path of a Hero (Part 5)
If you've been moving the chains on the quest "Task: Path of a Hero" and got the Email from Hakim Barakat, the producer of Keri's documentary, you'll find him on the Docking Bay level of the Nexus. Chat with him and he'll tell you that the Asari journalist got herself into a bit of legal hot water, and the word of the Pathfinder might just get her out of trouble.
Travel to Operations (how convenient!) and talk to Keri, who is busy filling up a prison cell. She'll have a spell of doubt concerning the value of journalistic objectivity, after which she'll thank you for visiting her, and the quest will go dormant once again.
Now that you're in Operations, you might as well meet with the leaders of the Initiative and update them on the most recent developments. Depending upon your choice concerning the Krogan or the Salarians, things could be quite tense - Kesh takes a lot more offense if her people died than Tann will. After making a statement concerning your actions, Ryder will explain the importance of Meridian, and the feckless Initiative leaders demur at the thought of any decisive action. While the surviving ranking Salarian from Ark Paarchero will vouch for you, Director Tann pulls rank and ends the discussion.
Subterfuge seems like the only way to get to Meridian in a timely manner, but before you can finish conspiring you'll be told about a development concerning your sibling. Don't worry, the fate of the Initiative can wait - it's a good thing, too, because you'll be forced into a conversation with your sibling. Unfortunately, they're in no condition to help out, but at least you can chat with them about developments in Andromeda, and learn some family history.
After you're done chatting with your sibling, leave the Cryo Bay and return to the Tech Labs on the second floor of the Docking Bay level. Here you'll conspire with the any Pathfinders (or aspiring replacements) you may have found across the Heleus cluster and the Nexus's resident scientists. Looks like you'll have to rely on new, experimental technology and direct insubordination... but hey, isn't that what being Pathfinder is all about?
With that, you're done in the Nexus, time to return to the Tempest. Once there, interact with a console on the eastern end of the Research Room to build the Ghost Storm Technology that'll hopefully cover your approach to Meridian, then head up a ramp to the Vidcom table an use it to call a crew meeting. After discussing the plan with your crew you'll be free to travel to the Civki system - to Meridian.
Now is a fine time to deal with any new sidequests that remain unresolved, especially new ones that popped up after escaping from the Archon's flagship. These quests will be bundled together in the section "Questing Post-Flagship". If you want to continue on with the main story, instead, simply skip ahead to "The Journey to Meridian - Fighting for Control".