No, these Star Trek characters don't need their own series
Star Trek has a plethora of characters to pull from if it's looking for potential series. Some, like Jeri Ryan's Captain Seven of Nine, we are hoping become a reality. That said, there are some characters that aren't strong enough for their own series. Recently, Chad Porto wrote about three characters he had in mind that could get their own series, and like we do here at Red Shirts Always Die sometimes, I disagree whole-heartedly with him.
Garrett Wang's Harry Kim was a great character on Star Trek: Voyager, but he remained an ensign throughout the entirety of the series. Thus, we didn't get a chance to see him really become a strong character. Even if he were to be promoted to captain in canon, a series about Captain Kim would be difficult to get off the ground. Kim's strength was in his ability to follow orders and give Captain Janeway [Kate Mulgrew] what she needed when she needed it because that's how he was written. Putting him in a starring role wouldn't guarantee fans would be able to accept his status as a captain as we never got to see his trajectory. Now a series with him and Tom Paris [Robert Duncan McNeill]? That has some definite possibility.
The other character Chad mentioned was George Kirk, Captain Kirk's brother who actually died on Star Trek: The Original Series but has been brought back alive on Star Trek: Strange New Worlds. We know next to nothing about this character, and Strange New Worlds hasn't made him all that interesting. On top of that, it would be difficult not to constantly compare him to his brother. Captain Kirk would always come out ahead.
And then there's Chad's final choice—Dr. Katherine Pulaski. He was asking what we knew about the doctor. Not much, and honestly, not too many fans wanted to know more. She'd taken over for Dr. Beverly Crusher, and that already put her in a bad position. Add in her surliness and conflict with Data, and she just wasn't an entirely likeable character. The Next Generation didn't do much to give her any redeeming qualities so having an entire series wrapped around this character just sounds like a mistake waiting to happen.
That doesn't mean Star Trek shouldn't take a look at some of its other characters to mine for exciting positions or guest-starring roles. It does mean the franchise should be careful about who it choses to bring to the forefront. Sometimes, it's best that we don't learn more about the characters that haven't been explored.