It is an exciting time for superhero films and female representation. If all goes as expected, all major MCU and DCEU offerings will be headed by females. Birds of Prey, Wonder Woman 1984, Black Widow, Falcon & The Winter Soldier and The Eternals are all being directed by women. During that year, it seems as though Supergirl will be shooting in front of cameras as well.
According to Forbes, Supergirl will be starting production during the first quarter of 2020 alongside Matt Reeves and Robert Pattinson's The Batman. Furthermore, casting for Kara Zor-El should be revealed in the coming months. This makes a 2021 release date, similar to The Batman, very likely.
Not many details are known about the project, but it is rumored that Warner Bros. is looking for a female director to shoot the film, in addition to making Kara the new face of the DCEU.