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?
As a Relaunch Litverse fan, I really liked the introduction of the competing Typhon Pact as a way to bring in a number of the less profiled species.
Having a different kind of interstellar government from the Federation in a Cold War rivalry for planets and civilizations was an interesting backdrop for the entire era. Creating an opponent that brought together a number of the less known species including the Breen, Tzenkethi, Tholians, Gorn as well as remnants of the Romulan Empire was inspired.
We never got to see as much of the Typhon Pact in the books as I would have liked. The concept though was inspired and one that would fit well in the early 25th century portrayed in Picard.
As for the Sheliak, the novelverse has them in conflict with the Breen for additional complexity.
The newest era of Trek hasn’t hesitated to integrate some of the more successful experiments from the novels, including Una’s name and Illyrian genetic modifications. The Typhon Pact of the Litverse has a lot to offer without being a direct competitor to the world building since Nemesis.