In Thomist philosophy, the intellect is a power of the soul, not the soul itself, and the soul is the principle of what a living material being is.
My understanding of Thomist philosophy of the mind is that the the Intellect, for one, is not all of our consciousness, but the ability of the person to abstract from particulars to understanding those concepts universally. And it’s not an immaterial part interacting with material parts, but rather a faculty of a human being as a whole. An " emergent property" (kind of), rather than a part. We’re a whole which is something new and not just the sum of parts. It’s just in the nature of a human to do this by virtue of being human. It’s not mechanical, as Descartes and those who came after him conceived it, but is better understood with Aristotlean conceptions of causation.