You really ought to go right now and read the whole of the de Regno, because it’s amazingly clear and simple.
Because the priesthood of the gentiles and the whole worship of their gods existed merely for the acquisition of temporal goods (which were all ordained to the common good of the multitude, whose care devolved upon the king), the priests of the gentiles were very properly subject to the kings. Similarly, since in the old law earthly goods were promised to the religious people (not indeed by demons but by the true God), the priests of the old law, we read, were also subject to the kings. But in the new law there is a higher priesthood by which men are guided to heavenly goods. Consequently, in the law of Christ, kings must be subject to priests.
(source: Thomas Aquinas: De Regno)