Thought for supporting character.
Genin medical ninja. A few years older than the rest of the group. She was never promoted to chunin... Basically, because she lacks leadership skills. She spends to much time evaluating options, which means he can't make a judgment call in the heat of the moment.
Honestly, she's fine if she never gets promoted... But she's also willing to be a seat filler if a team is being sent to the Chunin exam but is missing someone.
So if we're getting another player she could be introduced alongside the new PC as part of the "protective detail" and then serve as seat filler for the Chunin exam, meaning that Team 3 could enter and then Senko, Medic Nin, and New character enter as a temporary team.
Since she's older, she probably also has skills that could be shared with the team to compensate for the fact that they don't have a proper Jonin sensei. (which honestly makes sense to me. If the sound village doesn't have enough people for proper training, then it makes sense that they'd encourage people to teach what they know to others and to learn what you can from everyone.)