Deadline has reported that a new TV show based on the Arrowverse is in development based on Kate Kane aka Batwoman. Seeing as the character is already set to appear in the annual Arrowverse crossover, which will premiere this December it is not a surprise to see the character receive a potential spin-off series.
Keep in mind the series is up for consideration to be apart of the 2019 CW schedule so at the moment it is not confirmed that the series will officially premiere on the schedule. Caroline Dries and Greg Berlanti will serve as executive producers on the project.
Currently no other details are revealed at this time so stay tuned for updates.