George Leo Haydock, on Heb 9:15

And therefore he is the mediator of the new testament. [4] The mediator, so as to be our Redeemer, which applies only to our Saviour, Christ. Moses is called a mediator betwixt God and his people. See Galatians iii. 19. and 1 Timothy ii. 5. &c. The saints in heaven, and men on earth, may be called mediators in an inferior and different sense: but Christ alone is the mediator who reconciled God to men, by satisfying for their sins, and by a redemption from the slavery of sin. This sense, in which Christ is the mediator of the New Testament is expressed in these following words: that by means of his death, for the redemption of those transgressions which were under the former testament, they who are called may receive the promise of eternal inheritance; that is, Christ by his death, redeemed all men. He names in particular the sins of those under the former testament, to shew them that the sacrifices of the Mosaical law could not of themselves obtain a remission of sins, so that all saved from Adam, or that shall be saved to the end of the world, have their sins forgiven, and obtain salvation by virtue of Christ’s sacrifice upon the cross. He paid the ransom of their sins, and is the Redeemer of all. (Witham)