Chembaroness
We have read alot about how chembarons run the city down in Zaun and we have quite a bunch of champions who are hunting them for sports.
But we still don't have an actual chembaron champion in the game and that is really a shame in my opinion.
Additionally, Zaun still just has 2 female champions (out of 12, Zaun has the lowest female ratio of every region in the game), so I think making her female would be the best. Could also finally give us a gross looking girl in the game with chemtech augmentations.
Hikikomori data analyst
I want a champion who is socially awkward, who doesn't like to interact with people directly. I think this could work fine with someone sitting in their base and giving instructions. Such a champion could, for example, use cameras all over Piltover to gather information to give to the police.

In my vision, such a champion would also have a sentient hextech device. The brackern in the hextech crystal awakened and has taken control of the device, but the champion doesn't know this yet, since the device is supposed to have an AI, so they think they are actually still interacting with an artificial being.
Medic
We have some healers in the game, but they all have one thing in common: They use magic to heal. I would like to see a champion representing modern medicine, healing with hextech devices, syringes, bandages, and such. Could maybe use a syringe gun and have a similar playstyle to Moira in Overwatch, meaning that the champion has to deal damage to the enemy to fuel their healing, which would also make them more interactive.
Maid
I think a maid (in visual design) would fit well into Piltover and could give us another interesting personality trope. All champions more or less are self-determined, a maid could give us a "loyal servant". Someone who has sworn to do anything to guarantee the success of the house of her master, even if this means that they have to kill innocent people for it.
Just would really like to see this, since there were alot of maids in media I enjoyed as characters.
Criminal from Piltover
Looking through the roster of Piltovians, they all have the good or neutral alignment. I would like one evil champion from Piltover, this could be achieved in different ways. Maybe a serial killer, maybe a thief who doesn't care if he kills along the way.
Personally, I would enjoy a serial killer using a brutal hextech weapon. A chainsaw would be perfect, it is a weapon trope I was missing for a long time in this game and it would have a great contrast, since hextech usually is more elegant.