This scene presents these Humandrills as ferocious beasts intelligent enough to mimic certain human behaviours such using weapons and having ravaged this island to the point of it being entirely uninhabitable. And yet they do not dare come near Hawkeyes' castle. I'm going to assume it's because of Hawkeyes being there.
Now from what we've seen there's only two reasons that animals of any strength or even relative intelligence get scared of people to the point of not even wanting to be in their presence. The first is of course Conquerers Haki as we've seen even a few chapters ago and the second is probably bloodlust.
Let's go through the difference first, bloodlust is what Zoro has that he uses to intimidate people by instilling a sense of mortal danger from being around him. Conquerers Haki is exertion of will that can range from intimidation to taming animals entirely. I put the word "probably" before bloodlust above because we've never seen Bloodlust work on animals before but we've also never seen someone try and use it on animals either. The closest it's come to this is Cracker scaring the literal souls out of the homies in the Seducing woods from just his intimidation. But again you can argue those are still technically people at heart.
Back to the Humandrills then. They are considered somewhat intelligent so they sort of straddle the line enough for it to be possible for either Conquerers Haki or Bloodlust to work on them. So which one is it that's causing them to dread going into Hawkeyes' castle?
I don't think it's bloodlust for one main reason. That doesn't match Hawkeyes' personality. By that I mean Hawkeyes is generally not a bloodlusted person to the point that he was even surprised Zoro was so much like that when they fought. Hawkeyes does have an intimidating personality but that's mostly due to how he carries himself and his position and not that it feels like he wants to kill you at any moment.
That leaves Conquerers Haki as the last option as to why the Humandrills are so deathly afraid of even coming near his property. This also fits more into how most of the scenes play out. For example in the panel above, Hawkeyes is standing right next to the Humandrills and they aren't running away. They aren't approaching of course but they are also not running away. What they specifically fear is coming near the castle. This fits something that Conquerers Haki more so can do since its projecting ones will over another. Bloodlust is plain and simple murderous intent therefore it can't create as much variety in reactions to Hawkeyes. The Humandrills would fear Hawkeyes all the time and not just specifically fear not coming to the castle. It's Conquerors haki that can accomplish that by specifically making the Humandrills not come to his castle through enforcing that will upon them to the point that they wouldn't go to his castle even when he wasn't on the island at all.
The conclusion from this is that Hawkeyes has Conquerors haki due to how these seemingly ferocious animals respond to him.
NOTE.
Theres a few things that are unconnected to this scene that still support Mihawk having Conquerors haki.
1. Later on we learn that Hawkeyes now has the Humandrills working for him in his farm so he essentially tamed them somehow over the two years. We know Humandrills would naturally mimic peacful behaviour if they see it but Mihawk has been a peaceful guy of sorts from the get go and they never mimicked him. It's likely their constant aggression had to be tamed first so that they can observe the peaceful behaviour and then mimic it. This is possible with Conquerors haki.
2. Zoro says that Luffy having Conquerors haki was kind of a pre-requisite for him to respect him as his leader therefore he for some reason has already associated Conquerors haki with people worth respecting before the time skip even begins. The only other person he saw with this was Silvers Rayleigh and we have no indication that he had such a profound impact on Zoro that he would change Zoro's entire criteria of who to respect. The only other person we know Zoro looks up to is Hawkeyes and so this mindset could only have been instilled in him if Hawkeyes has Conquerors haki as well.
That's about it. What do you guys think about these seemingly subtle cues that Oda may be dropping?
Simple quiz :
