One of the fascinating things about this "third generation" of Star Trek (starting either with Star Trek 2009 or with Discovery) is the way the Star Trek universe has started to knit itself closer together by referencing existing backstory. For example, Discovery wholeheartedly embraced the idea that Andorians and Tellarites are key Federation members and should therefore be highly visible in Starfleet, building on lore originally implied in TOS, largely ignored by TNG, DS9, and VGR, and re-embraced by ENT. Prodigy, for its part, leaned very heavily on VGR for its worldbuilding source material.
This has also produced some interesting quiet exclusions from recent stories -- not to suggest they've been "decanonized" or anything like that, but clearly have been deprioritized. The Tholians come to mind as a ready example of this. Like the Gorn, they debuted in TOS, received stray mentions in DS9, before making an on-screen return in ENT. I wonder if the SNW writers considered using the Tholians but balked at a villain that had such different atmospheric requirements, and all the consequences that entails in terms of dramatic presentation. The Denobulans also seem to fall into a similar bucket; outside of a pair of appearances in PRO, they have received nary a mention since ENT.
Then of course we have the lengthy list of "one-off" civilizations, including the likes of
-the Sheliak
-the Husnock
-the Tzenkethi
-the Jarada
-the Miradorn
And in terms of "underexplored corners", I've only been focusing on the civilizations, but there are any number of other corners we could poke into. The Department of Temporal Investigations, the Corps of Engineers, the Federation Council, the Lunar Colonies... the Trekverse is littered with these little crumbs all over the place -- tiny seeds of ideas that suggest opportunities for imagination.
For my part, I would love to learn more about the Sheliak. For one thing, they seem like they would benefit from the advances in CGI over the last 30 years. But I like that they seem equally matched to the Federation in terms of strength, and that their hyperfocus on legal compliance gives them a generally underused "hat" to wear in the Trekverse. They have some similarity to Vulcans, but taken to an extreme, and layered in with real disdain for "lower life forms" that I think would make for a fascinating "adversary" -- I'd love to see Captain Pike or Captain Seven in a verbal jousting match with a Sheliak commander.
What is an underexplored corner of Trek lore that you think merits exploration?
I'd love to see more about the cultural and social revolutions which occurred in Ferenginar which were happening in the background of DS9 that resulted in the first Ferengi to be a trade union leader becoming Grand Nagus.
I think Nagus Zek and Moogie were working on ways to modernise Ferengi culture but the realpolitik of it means it can't just have been the two of them. I feel like there was a coalition of feminists and Ferengi workers in the proletariat growing in popularity.
Ferengi's seem to have been isolated from the Dominion War but it doesn't mean they weren't impacted by it, as the 3 biggest Empires closest to them were all actively in full scale war mode. I also think it's likely that prior to the war there may have been a kind of Gold Rush into the Gamma Quadrant which left many Ferengi investors overextended when the war started and the quadrant was cut off.
I think Zek and Moogie were trying to reform in this context. It's Russia in 1916-17 without the overt involvement in the war.
Ferengi workers and women, surrounded by the cultural hegemony of the Federation must have been causing strikes, protests and riots in the background, and the wealthy class of Ferengi were weakened due to their gamma quadrant investments failing.
While Rom was radical to lead a strike in the first place, it's possible he was seen as a moderate by the time of Season 7 after a few months of continuous disruption to Ferengi economy and politics. Also as a hero of the Allies fighting the Dominion who saved millions of lives with his role in keeping the wormhole closed and the resistance, he'd have a good diplomatic influence to regain trade with those powers and access to DS9 as a port.
So my working theory is that there was a gradual revolution in Ferengi culture, and that a coalition of Ferengi trade unions, feminists, Federation enthusiasts and socialists and democratic reformers were able to claim victory at the same time as the war ending.
But of course the FCC and the power of Capital amongst the elite must still have been immensely strong. 100% of a culture won't change overnight - but however the Ferengi left coalition gained influence (I'm thinking at least a general strike and riots - why else is Zek's message to Quark so garbled that he thinks he will be the next Grand Nagus) Rom was seen as a good compromise by both sides. The FCC working on their prior intelligence will see him as the moron brother of minor barkeeper they may be able to keep in line and manipulate, and who at this time is less radical than demands of some Ferengi revolutionaries, but to the left he's hugely symbolic as their first trade union leader. Both sides also accept that diplomatically he's going to be popular with the Federation.
There's no way Rom gets to be Grand Nagus without massive social and political change, without some kind of Marxist dialectic happening in the background.
I think Rom is the Social Democratic compromise between various political movements and also the first wave of further integration into the Federation and its ideals.
But we only get the surface level information of it. I think there's at least a double episode in it. Maybe a future Ferengi Star Fleet officer in Discovery could retell this story of cultural evolution after first contact with a particularly capitalist new alien culture.