Jett Reno
If we're being fair and honest, Jett Reno is fairly underutilized. She's a fantastic character, who has a quip and snark to her that isn't seen often in Star Trek, but the reason we want to see more of her isn't because of the character. While Jett Reno (great name) has potential layers worth exploring, the reason we want to see more of her is due to her actress, Tig Notaro.
Notaro is one of the better comedians going today and is someone with a true dry, but impressive wit that really lands with all sorts of people. She's able to get people to relate to her, regardless if they have a similar background or not and if you can get people in a live audience to see themselves in you, you can do that on the smaller screen.
Having Notaro take over a show, or even star alongside someone, would give Star Trek fans a very likable, and very different type of character to latch onto. Imagine her palling around with Holly Hunter's character in Starfleet Academy. Her character could be annoyed to no end by Notaro's Jett Reno, or Jet Reno could mature as a teacher, but still be a bit more hilarious in the way she deals with the rambunctions cadets.
Either way, Reno would be someone we would love to see more of.