John Chrysostom

It was probable that many of those who were more weakly would especially distrust the promises of Christ because He had died. Paul accordingly out of a superabundance introduced this illustration, deriving it from common custom. Of what kind is it? He says, "indeed, on this very account we ought to be of good courage." On what account? Because testaments are established and obtain their force when those who have made them are not living, but dead. …

Homily on Hebrews 16 ↗

Oecumenius

"there must also of necessity be the death of the one who made it," This is what disturbs them, the death of Christ. For how, he says, can the one who has died give us the promises? Therefore, he turns and shows that we can only receive the inheritance and the promise if Christ has died. For if he had not died, he would not have made a will, so that we might inherit; (for it is indisputable that a will is in force only after death;) nor would we be worthy of an inheritance at all, as long as the enmity remains unresolved.

The Pseudo-Oecumenian Catena on Hebrews ↗

Thomas Aquinas

450. – Then (v. 16) he proves what he had supposed, namely, that the New Testament was confirmed by the death of Christ: first, he proves this on the authority of human law; secondly, on the authority of divine law (v. 18). 451. – He says, therefore: It has been stated that the New Testament was confirmed by the intervening death of Christ, because in order that a will [testament] be in force, the death of the testator must be established. …

Commentary on Hebrews ↗