The hawk perceives himself as a predator. He is proud of himself, stating:

It took the whole of Creation
To produce my foot, my each feather

He understands his relationship to the world as one of dominance. His attitude is arrogant and possessive towards it. He sees the earth as belonging to him, saying,

I kill where I please because it is all mine.

Three possibilities of what the hawk stands for are as follows:

First, as a "king" of the forest, a predatory bird that sits in the topmost branches of the trees, he could be seen as representing the upper classes in society and reflecting their sense of superiority and ownership over the rest of the world.

Second, he could represent the blindness of arrogance. By the end of the poem, he has revealed himself as believing he is in control of the cosmos, which certainly is not the case. He says,

Nothing has changed since I began.
My eye has permitted no change.
I am going to keep things like this.

Clearly a hawk is not a creature with that kind of control, no matter how he might delude himself. In this reading, his self-concept is ironic, and we can imagine him soon shot down by a hunter.

Third, the hawk could stand for brute nature. In this reading, he is the representative of primal, predatory nature that does not analyze or look to the past or future, but simply exists in the present moment. The hawk alludes to his lack of reflection and his reliance on brute force when he says,

There is no sophistry [arguing] in my body:
My manners are tearing off heads