John Chrysostom

For "we have an altar whereof they have no right to eat which serve the Tabernacle." Not as the Jewish ordinances, are those among us, as it is not lawful even for the High Priest to partake of them. So that since he had said, "Do not observe," and this seemed to be the language of one who is throwing down his own building, he again turns it round. What, have not we then observances as well (he says)? Yea we have, and we observe them very earnestly too, not sharing them even with the priests themselves.

Homily on Hebrews 33 ↗

Theophylact of Ohrid

Having said that there is no need to strictly observe dietary regulations, lest it seem that our way, free from such observance, is worthy of contempt, he says that we too have an observance, only not in regard to these foods, but to the altar, or the bloodless sacrifice of the Life-giving Body. …

Commentary on Hebrews ↗

Oecumenius

"We have an altar." Since Paul said that we should not observe foods, lest they think our offerings are shameful by being unobserved, he says: For do we not also have observances? But not of foods, rather of our altar, namely, of the unbloody sacrifice of the life-giving body. For even the very high priests of the Jews are not permitted to partake of this; for they who serve in the tabernacle, as it were, in the type and shadow, and not in truth. …

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

Then when he says, We have an altar, from which they have no power to eat who serve the tabernacle, he gives the reason, and it is quite subtle. For, as it is stated in Leviticus (chap. 16), on the tenth day of the seventh month the high priest entered with the blood of a heifer and a goat into the holies because of his own ignorance, and burned their bodies outside the camp. And because it was the priest's offering, the flesh was not eaten. …

Commentary on Hebrews ↗