Din Djarin becomes the owner of the Darksaber at the end of The Mandalorian season 2, setting up a potential clash with Bo-Katan Kryze for the ancient weapon. The unique lightsaber was revealed to be in possession of Moff Gideon in the season 1 finale, and it remained with him until "The Rescue". This is despite Bo-Katan being its last known owner as seen in Star Wars Rebels. Now, however, she is motivated to reclaim it, as revealed in her initial encounter with Mando in Trask. But things got a bit trickier with Din now being its rightful owner.
In The Mandalorian season 2 finale, Din sought the help of Bo-Katan and Koska Reeves to rescue Grogu from Moff Gideon. Knowing that the mission could benefit both of them as she could ultimately reclaim the Darksaber from the villain, Bo-Katan agreed and ultimately became instrumental in Mando getting back his child. Unfortunately, things didn't go as well for her as Moff Gideon devised his own plan to ensure that she wouldn't be able to retake the Darksaber. Instead of battling her, the Imperial die-hard battled Din instead, who bested him. According to the rules of the black-bladed lightsaber, Mando now owns it and if Bo-Katan wants to get it, she should defeat him first in a battle.
This makes for a difficult situation because neither Din nor Bo-Katan want to fight each other; it's also what makes Moff Gideon's plan very clever. Not caring about the Darksaber, Mando simply offered it to Bo-Katan, but for some reason, she refused it, acknowledging that she must earn it fairly according to the rules. This raised questions as she didn't have any issues when Sabine Wren handed it to her on Star Wars Rebels. Bo-Katan's choice effectively pits her and Din against each other since she's motivated to rebuild Mandalore and lead its people, and she's unable to do that without the Darksaber. That being said, there's no way that Din will die on The Mandalorian, so there's got to be a way for Bo-Katan to reclaim the weapon without killing him, and based on what's known, there are some few options. As seen in the duel between Din and Moff Gideon, the loser of the fight doesn't have to die; they only need to be defeated. Given this, Bo-Katan and Mando can simply engage in an environmentally-controlled battle, as if to see who's the better fighter between them. Whoever wins gets the Darksaber. The biggest caveat about this is whether or not Din would be interested in indulging the idea; as seen in The Mandalorian season 2 finale, he doesn't have any intentions of fighting her whatsoever.
Another potential way is for Bo-Katan to eventually change her mind and just take the Darksaber as she did with Sabine. The Mandalorian didn't reveal why she's reluctant to do it this time, but it may have something to do with what happened to Mandalore during her reign. Perhaps some questioned the legitimacy of her leadership because she was handed the Darksaber. Granted that in Star Wars Rebels, the people of Mandalore seemed to be supportive of her rule being the sister of Duchess Satine Kryze, and the Purge may have cast doubt on her ability to properly unite and move the Mandalorians forward. This could also explain why Moff Gideon knew that Bo-Katan will be faced with a big dilemma once Din acquires the Darksaber. Assuming that she's worried her people will continue to doubt her effectiveness as a leader if she's just once again given the weapon, Din can help her prove her worthiness by backing her claim; they can work in tandem in the hopes of building trust on Bo-Katan considering that Din unequivocally supports her.
Finally, there's also the possibility that Bo-Katan doesn't reclaim the Darksaber from Din at all. Depending on how The Mandalorian tackles this story, future seasons can revolve around Mando working on unifying their people with Bo-Katan's help, which is still in line with her aspirations. This is particularly plausible now that Din's mission with Grogu is supposedly done.