Rather than introducing a new character to replace Kate Kane as the protector of Gotham City, season 2 of Batwoman should see the cape and cowl taken up by Julia Pennyworth. This is due both to Julia's preexisting relationships with most of the core cast, as well as her training and connections, giving her everything she needs to seamlessly slip into the Bat-Suit.
When it was announced that Ruby Rose was leaving Batwoman after a single season, speculation briefly ran wild as to who would be cast to replace her as Kate Kane and how the show would explain Kate's new appearance in a Post-Crisis Arrowverse without doppelgängers. Few guessed that the showrunners would elect to retire Kate Kane's character completely and introduce a new character who would somehow prove their worthiness to fill Kate's boots and integrate herself into the notoriously secretive and insular Bat Family at the start of Batwoman season 2. This made little sense to most of the fandom, particularly when the show had already introduced the perfect replacement Batwoman in the form of Julia Pennyworth, the daughter of Bruce Wayne's butler Alfred Pennyworth.
First appearing in the Batwoman season 1 episode "Tell Me The Truth," and played by Christina Wolfe, Julia Pennyworth was introduced into the show as a member of the United Kingdom's Special Reconnaissance Regiment. Posing as a Krav Maga instructor and using an alias, Julia approached Kate Kane in 2013 while she was in the middle of traveling the world seeking combat tutors. Julia did this at the request of Bruce Wayne, who wanted someone to keep an eye on his cousin while she was in London. The two entered into a brief romantic relationship, which ended when Julia's cover was blown and she was attacked by old enemies who called her by her real name while she was with Kate.
Julia popped back into Kate's life seven years later, while chasing a notorious assassin called The Rifle to Gotham City on behalf of the SRR. However, it was revealed later in the season that Julia had lied about still being with the SRR and that she had been disavowed by the organization after she traveled to the pirate nation of Coryana and tried to broker a deal with the crime lord Safiyah Sohail in order to save Batwoman's life. Shortly thereafter, Julia was recruited into Crows Security and partnered up with Kate's ex-girlfriend Sophie Moore, romantically and professionally.
The chief reason why it makes more sense to have Julia become Batwoman than pass the mantle on to a newcomer is that Julia has already addressed the major problem any new Batwoman would face; integrating herself into the series and building relationships with the core cast as deep as those enjoyed by Kate and the other characters. The show established that Julia was a childhood friend of Team Bat's resident tech expert, Luke Fox, and that Lucius Fox was her godfather. Given how notoriously paranoid Luke is about letting anyone in on the secrets of the Bat Family and that he controls all of Batwoman's technology, winning his approval would be the biggest obstacle any potential Batwoman would have to face. Julia also developed a relationship with Sophie Moore as similarly complicated as the one Sophie shared with Kate and there has been some suggestion that Julia's relationship with Safiyah Sohail was also not entirely professional.
Beyond sharing Kate Kane's habit of entering into bad romances, Julia possesses all of the training required to become Batwoman. Indeed, she's already taken up the cowl once and ironically she did it so that Kate could be seen in the same place as Batwoman by Sophie Moore, who had begun to suspect the truth of Kate Kane's double identity. Sadly, it seems that Batwoman's showrunners are committed to their convoluted plan to replace Kate Kane with a new character, despite it making much more sense on every level for Julia Pennyworth to become Batwoman.