9:17 For a testament [is] of force after men are dead. As soon as a man dies, his last will and testament comes into force, but has no force whatever while he lives. The application of this is that Christ's testament, the new covenant, came into force when he died. The old covenant was in force to the cross; it was then nailed to the cross (Col 2:14), and Christ having died, the New Testament came into force. It has been urged against this view that the making of wills was not a custom of Israel. It was, however the custom of the whole Roman Empire, and Judea was now a Roman province. The Roman customs had made provinces of the empire familiar with the use of wills.
9:17 After he is dead - Neither this, nor after men are dead is a literal translation of the words. It is a very perplexed passage.
9:15-22 The solemn transactions between God and man, are sometimes called a covenant, here a testament, which is a willing deed of a person, bestowing legacies on such persons as are described, and it only takes effect upon his death. Thus Christ died, not only to obtain the blessings of salvation for us, but to give power to the disposal of them. All, by sin, were become guilty before God, had forfeited every thing that is good; but God, willing to show the greatness of his mercy, proclaimed a covenant of grace. Nothing could be clean to a sinner, not even his religious duties; except as his guilt was done away by the death of a sacrifice, of value sufficient for that end, and unless he continually depended upon it. May we ascribe all real good works to the same all-procuring cause, and offer our spiritual sacrifices as sprinkled with Christ's blood, and so purified from their defilement.