The third season of Star Trek: Discovery has been one full of firsts and changes for the USS Discovery and the Star Trek universe. The Federation isn't what it used to be, having gained some members since Discovery made its jump into the future and lost a few since the Burn. Closer to home, Discovery finally named a new, permanent captain for the first since learning that Gabriel Lorca was an imposter from the Mirror Universe. Saru took command of the Discovery and gave Michael Burnham the role of his new first officer as she returned to the ship. That proved to be a fortuitous move as proving Discovery's value to the new Starfleet required Discovery to embark on a mission with its first officer in command.
Admiral Vance, the head of Starfleet in the 32nd century, was suspicious of time-traveling Discovery. After all, it wasn't that long ago that Starfleet fought the Temporal Cold War and eventually outlawed time travel entirely. To prove the ship's value and dedication to Starfleet's mission, Saru and Burnham volunteer Discovery's services to save many lives. The ship will use its unique spore drive to retrieve seeds from the Federation's seed vault ship. Those seeds were vital to discovering the cure to a sickness ravaging a group of galactic travelers. But Vance only agrees because Saru says he'll stay behind at Starfleet headquarters. That puts Michael Burnham in command of Discovery.
It's interesting timing. From the first episode of Discovery, Burnham always wanted to be in command of a starship. She had the opportunity to argue for that role aboard Discovery and gave it up willingly to Saru. Now she has her first command mission (that we've seen; we don't know if a similar situation ever arose while she was Capt. Georgiou's Number One aboard the USS Shenzhou).
She handles herself well. She gets Discovery to its destination, sees that her bridge crew gets the ship through an ion storm in one piece. She then leads the away team that boards the seed ship, along with Dr. Culber and Cmdr. Nhan. She gets a sense of the crisis onboard, relies on her science team to figure out a solution, talks a grieving man into doing the right thing, and parts ways with Nhan. Upon returning to Starfleet HQ, Vance welcomes Discovery home. All in all, a successful mission.
Burnham may lose whatever points she scores for a job well done as the preview for next week's episode suggests she's going rogue to help out her friend, Cleveland Booker. Where that leaves her in regards to Discovery and Starfleet remains to be seen.
New Star Trek: Discovery episodes stream Thursdays on CBS All Access.