Warning: MAJOR SPOILERS for the recent Supergirl episode 'For the Girl Who Has Everything' lie below! Continue at your own discretion!
So. There it was. The major death that no one was expecting. I mean, sure we know that in the past, Alex has told Supergirl "This is war. And to win a war, sometimes, the enemy has to die." But who was expecting Alex to be the one who caused said enemy to die? That's right, Alex murdered Kara's aunt, Astra, (the commander of the Kryptonian forces that escaped from Fort Rozz) using a kryptonite sword.
So, obviously, with Astra gone, her husband Non is now the commander of the Kryptonian forces. But what does this mean for our Girl of Steel? We know that from the beginning, Non has had no great love for his niece. Indeed, the only thing that has prevented him on multiple occasions from killing her in cold blood is Astra. With her out of the picture, Non has now been given the carte blanche he needs to get at Supergirl without upsetting his wife.
Non always viewed Astra's protection of Supergirl as interference and guilt over her sister Alura, but Astra has always stood up to him, saying that "Kara is not like her mother. She can be made to see reason," prompting her husband to respond, "I sometimes wonder if ANY of the women in your family can." Non, unlike Astra, has absolutely zero qualms about murdering Kara, regardless of the fact that she is family.
As far as Non is concerned, Kara is nothing more than a hindrance and a distraction. He wouldn't think twice about destroying her. The few times that he and Kara have been on screen together, every line of dialogue he says to her is absolutely dripping with disdain. That said, it's going to take a whole lot more than Non and his small band of Kryptonians are expecting to deal a final deathblow to Supergirl.