Hebrews 9:15  And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressions that were under the first testament, they which are called might receive the promise of eternal inheritance. 

‘And for this cause he is the mediator of the New Testament.’To this end, Christ became the mediator of the new covenant, that through His death sins could be remitted and men be given eternal inheritance.

‘Mediator’ [Greek: mesites] mediator, Moses (John 1:17; Deut. 5:1-33). Christ is the mediator of the new covenant (8:6; 9:15; 12:24; 1Tim. 2:5). This again is proof that Christ and God are separate Persons, for a mediator is the middle person mediating between TWO other persons who are at enmity with each other.

‘New Testament’ [Greek: diatheke] Translated as “covenant” 18 times (8:6-10; 9:4; 10:16, 29; 12:24; 13:20; Luke 1:72; Acts 3:25; 7:8; Rom. 9:4; 11:27; Gal. 3:15, 17; 4:24; Eph. 2:12;) and “testament” 12 times (7:22; 9:15-20; Matt. 26:28; Mark 14:24; Luke 22:20; 1Cor. 11:25; 2Cor. 3:6, 14; Rev. 11:19).

‘By means of death’ – It was only through death that man could be saved, for death was the penalty for sin (2:9-15; 9:15; Matt. 26:28; Rom. 5:6-11; 6:10; 14:9; 1Cor. 15:3; 2Cor. 5:14-21; Col. 1:14-22; 1Pet. 2:24).

‘For the redemption of the transgressions that were under the first testament.’Christ died to redeem the Old Testament saints who looked forward to the cross by faith as we look back to the cross by faith (11:1-40).

‘They which are called might receive the promise of eternal inheritance.’ Final calling and election are based upon meeting the terms of God in our period of probation. It is at the end of a life of conformity to the gospel that we receive the eternal inheritance (1Cor. 9:25-27; 2Tim. 4:8; Jas. 1:12; 1Pet. 1:4-5, 9, 13; 2Pet. 1:4-10).