Theophylact of Ohrid

"In childhood" not by age, but by knowledge of God. And by "elemental principles" of the world he means new moons and sabbaths, because these days come to us from the course of the moon and the sun. Therefore those who now subject us to the law thereby make us children and enslave us to the elements of the world, even though we have already become perfect men, and sons of God, and stewards, and lords. …

Commentary on Galatians ↗

Oecumenius

"when we were children." He says " children " not in respect of age but of knowledge of God, indicating that God had willed to grant these things from the beginning, that is, adoption as sons, but that we are responsible for the delay, being children in our minds. Having then been permitted, by God's patience, to be enslaved to the elements, that is, to the course of the sun and the moon. …

Commentary on Galatians ↗

Jerome

And so we too, when we were little, were enslaved under the elements of this world. He called the elements of the world, the same ones he had mentioned before as tutors and guardians: because we were not yet able to receive the coming of the Son of God, we were being trained in the midst of them. Some think that these are angels who govern the four elements of the world: namely, earth, water, fire, and air: and it is necessary that before anyone believes in Christ, they be governed by these arbitrators. …

Commentary on Galatians ↗

Thomas Aquinas

He applies this simile when he says, "So we also, when we were children, were serving under the elements of the world." First, he applies it as touching the Jews; Secondly, as touching Christ (v. 4). He says therefore: I say that as long as the heir is a child he differeth nothing from a servant; so, we Jews also, when we were children in the state of the Old Law, were serving under the elements of the world, i.e., under the Law which promised temporal things—"If you be willing, and will hearken to me, you shall eat the good things …

Commentary on Galatians ↗