It doesn't read very bird of prey yet, but I don't see how you could improve on that really. I feel like the problem is the beak. The black forehead and black beak kind of meld together, I would really highlight the beak as that's what screams predator to me.
I think that may just be an issue with the Osprey in particular due to its color scheme. I was going for an easily recolorable sprite so I could bash out flavor art real quick and that color scheme (gray and black) was easy to create a pallet for. Here is the same sprite but colored and slightly modified to be a Harris Hawk:
Does that improve the read? Here it is with the player character for size. The sprite is about 1.6ft tall in game scale.
A second point is shoulder or arm. Bird on shoulder = pirate, bird on arm = always hunting bird. If you manage to get the bird on my character's arm, even if it looks like a parrot, I'll still think hunting bird.
I didn't think about that and its a really good point. This is still 100% an art project but since form follows function the in game RPG rational is that these would be hyprid pets/equipment. Some birds would act as passive stat boosters that are equipped to the shoulders slot. Parrot gives charisma, Raven gives constitution, owl gives intelligence, etc. Other birds would be more like weapons and be equiped to an arm slot, and they could be actively used for some utility as a glorified Zelda boomerang such as the Osprey being able to get to deep water fish spots without a boat, the Harris Hawk can be used to hunt small animals without spooking them, etc. Then the bigger eagles can be actual offensive weapons verse mobs.
That's where I am coming from.