Theophylact of Ohrid

And, behold, there appeared unto them Moses and Elijah talking with Him. What were they talking about? "The ending," says Luke, "which He should accomplish in Jerusalem" (Lk. 9:31), namely, the Cross. Why did Moses and Elijah appear? To show that He is Lord of the law and of the prophets, and of the living and of the dead. For Elijah was a prophet and still lived, while Moses was a lawgiver and had died. …

Commentary on Matthew ↗

Jerome

And behold, Moses and Elijah appeared to them, talking with him. When the scribes and Pharisees tested him, seeking signs from heaven, he did not want to give them, but refuted their wicked request with a prudent response. But in order to increase the faith of the apostles, he gives a sign from heaven, with Elijah descending from where he had ascended, and with Moses rising from the dead. This is also commanded to Ahaz through Isaiah, to ask for a sign from above or from below (Isaiah 7 and 2 Kings 2). …

Commentary on Matthew ↗

Hilary of Poitiers

Also that Moses and Elias only out of the whole number of the saints stood with Christ, means, that Christ, in His kingdom, is between the Law and the Prophets; for He shall judge Israel in the presence of the same by whom He was preached to them.

Catena Aurea by Aquinas ↗

Thomas Aquinas

And behold there appeared to them Moses and Elijah. And why did they appear? Chrysostom assigns the reasons. The first reason is to confirm the faith of the disciples. He had asked above: whom do men say that the Son of man is? etc. And they said: some, Elijah, etc. But in order to show the difference between himself and them, he willed to bring them forth; Psalm 85:8: there is none among the gods like unto you, O Lord, etc. The second reason is to confute the Jews. …

Commentary on Matthew ↗