Lord Haruka doesn’t approve of Zen and Shirayuki associating with each other. He doesn’t trust her because she’s a commoner and he thinks she’ll take advantage of Zen. Obi is his accomplice. At first he tries lies to keep her out of the palace then he tries to scare her with an arrow.
Shirayuki doesn’t back down. She refuses to give in, instead attempting to get to Zen to talk to him directly. This also causes her to be even more determined to be court herbalist so that she has a legitimate reason on her own to be in the palace instead of relying on Zen. I also love that Zen fully supports her.