From there, the ring selects its new wielder within that sector, and whether Hal gets to meet Abin Sur like he did in the comics and the 2011 Green Lantern movie or doesn’t come face to face his predecessor, he would be transported to Oa for training, hence why a Green Lantern isn’t aiding Batman, Wonder Woman, Aquaman, Flash and Cyborg in battling Steppenwolf and the Parademons.
If the Green Lantern is Abin Sur, then his demise could potentially serve as an adaptation of Hal Jordan’s origin.
If the Green Lantern who is supposed to look after that sector is an alien, then they’re most likely dead, as DC wouldn’t risk killing off one of the human Green Lanterns so soon.
Abin Sur tries to stop Steppenwolf from reaching Earth, and is fatally injured in the process.