In his short time on Game of Thrones, Euron's proven himself to be cocky, sadistic, and full of bloodlust. He's definitely not known for his kindness or sense of impulse control, so it was surprising to see in the season eight premiere that he kept Yara alive. After he takes his niece during the raid on her Iron Fleet in season seven, it seems like Yara's a goner, but she lives through the premiere and is even rescued by Theon while Euron's off having a dalliance with Cersei. That begs the question, why did he spare his niece's life?
Getting inside the mind of Euron isn't something anyone wants to do, but he shares with Yara one reason for keeping her alive during the premiere: she gives him someone to talk to who can talk back. As revealed in season seven, the older Greyjoy cuts the tongues out of his crew's mouths in order to prevent them from communicating with each other. His reasoning is that without tongues they can't mutiny against him. That's why his ship is called The Silence. Despite his commitment to keeping his crew in line, Euron loves to talk, and his twisted methods mean he never has anyone to verbally spar with on his voyages. By keeping Yara alive, he ensures that at least one person on his ship can talk back when he goads them.
While that's the motive that he offers to Yara, there's no doubt more to Euron keeping her alive than he lets on. For a person as strong as his niece, being held captive has to be hell, and Euron is all about serving up his own special brand of torture. On another level, he seems to have a begrudging admiration for Yara. That doesn't stop him from torturing her, but her refusal to yield to him is just the kind of challenge that the pirate enjoys. Keeping her alive is also a way of toying with Theon — something he gets a perverse sense of pleasure from.
One thing we can be sure of is that there's nothing sentimental about Euron's motives. He wants to be the one and only Greyjoy left standing when this war is over, and he's more than happy to cut down his niece and nephew to achieve his goal. It's Euron's arrogance that allows Theon to successfully free his sister and put her on a path to take back the Iron Islands and potentially create a stronghold for Daenerys and her people. He may have left her alive to entertain him on those long, quiet voyages, but when he discovers his nephew's coup, Euron will surely be after both of their heads.