Perez has naturally sharp features, and has developed a naturally cautious approach when it comes to dealing with others. No doubt thanks to his former nanny and the Empress. It's easy to mistake the stare from someone like that with hostility, but it also may not be that far from the truth in his case. He doesn't necessarily have to be jealous, but he's probably sizing up Clerivan.
I'm guessing it's because Clerivan left the Lombardi family for the Pellet Union, since no one knows he actually works for Tia
Perez doesn't actually know that he works for Tia, right? This may be a good motivator for looking at Clerivan with suspicion. Since given his experiences and how fond he is of Tia, he's probably taken it upon himself to look out for people who might betray her and Lombardi.