Brainiac in Prison & Doomsday on the Loose
Though Brainiac is no longer the show's main villain, the "collector of worlds" is far from dead. He'll presumably be Seg-El's biggest threat at the start of season 2. That means Seg will have to deal with a vengeful Brainiac until he finds a way to escape.
When Seg finally does leave the prison dimension, what's to stop Brainiac from tagging along? Defeating Brainiac a second time will surely be a significant challenge for Seg, who won't have the aid of his allies. There's a good chance Brainiac will also find a way out, even if it doesn't happen soon. Judging by the captive American city in the finale, Brainiac will eventually break out and find his way to Earth.
Even if Brainiac remains a prisoner of the Phantom Zone, the people of Krypton will have their hands full with Doomsday, a creature so powerful that Zod originally intended on using him to kill Brainiac. And now Doomsday is free after he liberates himself from his prison in the last scene of the finale. We know from both Doomsday's comic book background and from remarks made in previous episodes that there may be no way of stopping the monster from destroying everything in his path. General Zod may have to team up with the resistance to prevent him from killing everyone on the planet. Unfortunately, Doomsday may prove to be unstoppable.
Expect to Visit More Planets
One of the last scenes in the finale was set on Earth and showed an American city that was apparently under Brainiac's control. A Zod statue was seen in the vicinity, which indicates that Earth was conquered by Zod at some point in its history. This marks the first time the series has shown us another civilization outside of Krypton. Unless there's a time jump, season 2 could begin with Adam Strange wandering around Earth until he decides to travel back to Krypton.
Zod's speech to the people of Krypton about galactic conquest could give fans a clue of where the series is heading. Kryptonian society previously rejected the existence of alien life, but the rise of Brainiac quickly changed their minds. Zod is determined to expand Krypton's influence by conquering other planets, so season 2 could explore this idea and send Zod and his new empire into war with other alien civilizations. Val-El may hold the key to finding these planets, since his time in the Phantom Zone has granted him knowledge of other places in the universe.
Exploring other planets is something that's already been discussed by showrunner Cameron Welsh, who has expressed an interest in visiting Hawkman's home planet, Thanagar, which is the home to a technologically advanced society. The Green Lantern Corps and the Omega Man are also on the table. Considering that Krypton exists in a "fully-realized DC Universe," the door is wide open to explore a range of other planets and civilizations from the comic books; although, at the end of the day, the crisis on the show's titular planet Krypton will still be at the heart of season 2.
The exact release date for Krypton season 2 isn't known yet, but it will be back in 2019. There's already a teaser, so if it's in-line with season 1, you can expect it in March 2019.