Cara Dune (Gina Carano) turned down an opportunity to join the New Republic in The Mandalorian season 2. If she had accepted, she could have proved to be a valuable asset for the New Republic as they continue to fight against the remnants of the Empire.
In The Mandalorian season 1, Mando (Pedro Pascal) encountered former Rebel shock trooper Cara Dune while looking for a place to lay low on planet Sorgan. After teaming up to take down an AT-ST, the two reunited toward the end of the season to fight the Empire on Nevarro. The season ended with Cara staying behind to help Greef Karga (Carl Weathers) rebuild the Bounty Hunter Guild. She returned in The Mandalorian season 2, episode 4, when Mando’s journey brought him back to Nevarro for some much-needed repairs on his ship, the Razor Crest. Alongside Greef Karga, Cara, and Mythrol (Horatio Sanz), Mando launched a successful attack on an Empire base.
At the end of the episode, Cara was approached by New Republic pilot Carson Teva (Paul Sun-Hyung Lee), who gave her a New Republic medal and invited her to join them. However, Cara declined a position in the New Republic. It’s likely that Cara could have helped them a great deal and would have benefited from such an arrangement, but it would seem that the character has become committed to her new responsibilities on Nevarro. Cara started her work with the Bounty Hunter Guild not that long ago, and it could be a job that she doesn’t intend to quit anytime soon.
There’s also the matter of Cara’s past. After the Empire fell, Cara transitioned from Rebel shock trooper to a member of the New Republic, but the work she did for them wasn’t something she enjoyed or cared about. Before, she was a soldier fighting for freedom, but once the civil war was over, she was being used for stopping riots and other tasks that didn’t give her much meaning. Though Teva makes clear Cara could help them with the fighting in the Outer Rim – which is perhaps something she’d be more inclined to take part in – her past experiences may have given her a lack of enthusiasm when it comes to the New Republic.
Another reason is that Cara Dune is a bit of a loner. She points this out to Teva when she says she’s not a “joiner”. It’s true that Cara works with the Bounty Hunter Guild, but as the Marshal, she has a certain degree of authority and may not necessarily take orders from Greef Karga. Her situation would be different if she worked for a galactic organization like the New Republic. The independence that she enjoys with the Bounty Hunter Guild feels better suited for her character in The Mandalorian. Even so, it's always possible that one day Cara will rethink her decision and take Teva up on his offer.