Gideon Seyetik. Kiley could be so over the top sometimes.
Among the space hippies, I was intrigued by Tongo Rad, the purple-haired guy. One moment, he’s spouting starry-eyed idealism with the rest of them, but when the chips are down, he’s capable of cold-blooded cynicism.
For sheer cheesiness, Shahna.
Dig that green hair! 
Elaan of Troyius comes in a close second.
Sheet plastic g-strings, cool! 
A lot of great ones here and I’ll add Kieran MacDuff, first officer of the Enterprise-D
TOS:
Any character played by Janos Prohaska: Yarnek, Gumato, Horta, anthropid ape/humanoid bird
Gorn played by three uncredited actors and Ted Cassidy’s voice:
This episode also features a memorable performance by Carolyne Barry – better known as the “girl with the horn-rimmed glasses” on Shindig - as the Metron; a triumph of quirky casting, androgynous make-up and Vic Perrin’s dubbed voice.
NG
After Picard and Riker phaser the shit out of bad guy Remmick, a hideously disgusting alien parasite is revealed in “Conspiracy.” It is a personal favorite character of mine (it’s also kind of icky, so blurred):
From IMDB: “A mold of Paul Newman’s face was filled with raw meat and then blown up to create the effect used when Picard and Riker fire on Remmick, but both Rick Berman and Peter Lauritson were concerned that it was too graphic. Dan Curry invited his six-year-old son to watch the episode in order to test how children would react to it; the boy reportedly liked it so much that he suggested the creation of a Remmick action figure whose head would blow up by pressing a button. This resulted in Berman deciding to air the episode uncut with the full sequence included.”
Let’s not forget the Eymorgs!
Amon Marritza/Gul Darheel from the Deep Space Nine episode “Duet”.
I submit for your consideration Shari yn Yem, a Pandronian from the Lower Decks episode “I, Excretus”, which could separate herself into her head, chest, and legs. She freaked out when the Cerritos went through anomalies.
Seriously, though…
Roberta Lincoln and Isis. 
You did say “single episode”, so Mudd is out.
I’ve seen that picture so many times, so I assumed I’d seen the episode. But then I found out about another character that I’d not ever seen, as I’d remember. She’s a woman who has this very deep voice that sounded like a changed voice (aka “masculine”) to my ears. I tried to look up if she was trans or if someone else dubbed her lines, but I couldn’t find anything.
I reserve the possibility of changing my mind later (especially if I can find a list of one-off characters). But right now I actually kinda liked the “Outrageous Okona.” I know that’s sacrilege, but I like him for the reasons people don’t like him. It felt like the actor was in on it.
But it’s possible that’s just hype backlash, and there’s someone better. And if we can stretch it to two episodes, then the clear winner is Robin Lefler.
Also an honorable mention to Amanda Rogers (the human Q). She’s the character that I right now wonder the most about what happened to.
There was a member of that species in the 1970s Trek animated series, as well, named Bem.
Chekov’s thrall Tamoon in “The Gamesters of Triskelion.” Played by Jane Ross.
She was part of a singing group called The Tri-Tones, so the character’s deep voice was presumably her own.
I can find no evidence that she was transgender, though she did die at the relatively young age of 53 in 1985.
Do you know if there are any clips of her talking? I’d just like to hear if that’s her normal voice, or she was deliberately lowering it for the effect. Maybe she’s just like those female voice actors who can do male parts.
I’ve always been fascinated by what aspects of the voice make someone sound male or female. (Also, the word today is transgender, not transsexual, as the latter is associated with porn).
Here is Jane’s biography at IMDb. She was in a number of works besides Star Trek.
Text amended, BTW.
Dr Miranda Jones from Is There In Truth No Beauty? partly because of her combination of intelligence and hawtness, but perhaps also because, if, as an actor myself, I can be said to have a signature role, it’s the Earl of Gloucester from King Lear.
Yeah, I saw that, but most of her credits seem to be bit parts that would be hard to look up. I just thought that, since you knew who she was, you might know some clips or something, like maybe where she spoke on an album or something.
But that’s enough of this sidetrack. I just couldn’t pass up asking since you showed the other big guest actress in the episode.
How about Terri Garr in TOS’s episode Assignment: Earth. Hot in a way, still interesting despite that, and a shapeshifting alien to boot.
Her hair alone is worth the price of admission.
Nitpick: Haughtiness, not hawtness.
Terri Garr was human. The shape-shifting alien was Isis.