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 thought the Miradorn were interesting. The twin bond that they have seems to suggest they have some kind of mental abilities, some way to connect the two people. They were listed as 'quarrelsome', could be an interesting mirror for the Tellarites, coming from a non-Federation species. They sided with the Dominion in the war, too, so they don't seem to think much of the Federation. Could make for an interesting antagonist.
edit: Thought about this some more. What if the twinned Miradorn didn't refer to brothers from the same mother? Perhaps their whole society consists of twinned people. Perhaps they have some sort of process where they bond two of their people together, for life, and that's how they run their world. Think of how dangerous an adversary that would make, there's always two of them. Even better if they have some sort of 2 person hive mind between them, so that they can work together seamlessly, even at a distance. Like some kind of organic grassroots Borg.