Defeating and killing Lion is already made it clear that he was strong.
It was the only thing Kai needed to really understand—that he could become stronger, much stronger than anything he imagined. Kai already proved to himself that he can achieve what his sister wanted from him.
No need to do it again.
Chester is a threatening individual, but he's not in a rush to do anything.
All he needed to do was to focus on his next steps.
And that is to become the Red Prince.
Getting into a tussle with Chester would only put him into more danger with the Chancellor, which he didn't want to do right now. Not when he was being watched closely. But there's a limit to Kai's patience.
Seeing how Chester ignores the safety of an innocent man made him lose it.
It clawed at his conscience, forcing the darker side of him to come out.
