We only see him when he interracts with her, and we get some hints on what he does behind the scenes. Also, his whole 'image' is a 'useless crown prince' so the nobles wouldn't suspect him, and he could do things without much hype at his own pace. I think the crown prince is just enamoured with Aria because he found an intellectual equal, they are both cunning af. He would've never shown interest in her if she was just some pretty girl with no brains (like Mielle, tho she ainkt that pretty imo...)