Agost was fuming. Not just at Alora, he was mad at Arihan too. If he becomes silent and lets the two be close, he would lose Alora.
If she didn't want to learn to ride the horse, he was ready to let her do anything without leaving her alone with Arihan.
Hence he followed Arihan to avoid him finding Alora first. Until he gets married to her, he has to keep her eyes & attention on him. So that she doesn't back out from marrying him.
Arihan went looking for Alora and got to know she was in her chambers. After hearing from Freya that Alora gets teleported whenever her emotions go all over the place, Arihan wasn't ready to leave her alone for long.
He knocked on the door and asked in an audible voice, "Princess Alora, are you there?" He waited for a few seconds for her to open the door but there was no response. He decided to let her know he was entering inside.