My recommendation would be the Kris Longknife series by Mike Shepherd.
Kris isn't a space mercenary, she's space military, and she starts off as a Lieutenant (and a Poor Little Rich Girl) but rises through the ranks over the book series. Some of her rise is a little unconventional because she has the money and the connections and the experience that those connections have brought her, but I liked her growth through the series.
Fair warning, the first book, 'Mutineer', has a scene in which Kris faces some people who've been attacked by bandits. I understand the scene caused some readers to NOPE out of there. It's not a trigger for me, although it was disturbing, but it may be for others. Since you've mentioned Elizabeth Moon and female space mercs, I'm going to assume you've read the Serrano/Suiza legacy and know Brun's storyline? It's comparable to that, but not described in the book in the present (as Brun's story does) but as something that happened in the past to the people Kris is speaking with.
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Kris isn't a space mercenary, she's space military, and she starts off as a Lieutenant (and a Poor Little Rich Girl) but rises through the ranks over the book series. Some of her rise is a little unconventional because she has the money and the connections and the experience that those connections have brought her, but I liked her growth through the series.
Fair warning, the first book, 'Mutineer', has a scene in which Kris faces some people who've been attacked by bandits. I understand the scene caused some readers to NOPE out of there. It's not a trigger for me, although it was disturbing, but it may be for others. Since you've mentioned Elizabeth Moon and female space mercs, I'm going to assume you've read the Serrano/Suiza legacy and know Brun's storyline? It's comparable to that, but not described in the book in the present (as Brun's story does) but as something that happened in the past to the people Kris is speaking with.