The chief point in view in the old and new covenants is to form and organize a community of people that are distinctively separated unto God. In Gods plan of redemption He decrees a people truly His own: The sheep never choose the shepherd, But the shepherd chooses His sheep! Jn 10:25-30, Exodus 6:7, Jeremiah 31:31-34, Hebrews 8:8-13 Heb 9:15
The intention of Christ’s death was to redeem those under the old covenant (first covenant) from their acquired sins. The question must be answered as to why the death of Christ was necessary for redemption from the sins committed under the old covenant and to what extent does His death benefit those under the new covenant? (I will venture to briefly touch on the subject)
First, the blood of bulls and goats offered by the High priest could not take away sins Heb 10:4. It required a more perfect sacrifice, Christ came as High Priest and mediator, entered the Most Holy Place, and offered Himself up to put away sin in order that he may secure eternal redemption Heb 7:22, Heb 8:6-7, Heb 9:11-12, Heb 9:26.
The mediator (Moses) of the old covenant could not offer up himself due to sin. It required God Himself to be the sacrifice without spot in order that He might be just and the justifier Heb 9:14, Rom 3:26.
It was necessary that Christ as High Priest and mediator to have something to offer in the inauguration of the new covenant, which is laying down Himself as the sacrifice Heb 8:3. The old covenant ceremonies served as a copy and shadow of Christ’s more excellent ministry as He fulfills the role of High Priest, mediator and offering Heb 8:5-6.
Heb 9:16-17 helps to answer this question in further detail. This passage concerns the actions involved in the ancient ceremony which (initiates) the covenant relationship according to v19. It specifically refers to the splitting of the carcasses and the pledging to death by the covenant parties (God/man). Gen 15:1-11, Exodus 24:1-8, Jer 34:17-22. The people would split the calf in two and pass between the two parts which symbolized the pledge between the two covenant-makers (God/man).
V16-17 May read: “For where there is a covenant, there exists the necessity of representing the death of the covenant-maker, for a covenant is made firm by death, since the covenant has no power at all while the covenant-maker lives”. By means of Christ’s death, the elect of God under the old covenant receive the promise of the eternal inheritance Heb 9:15. The covenant of eternal redemption (Heb 9:12) is inaugurated and ratified by the death of Christ who is High Priest, mediator and offering. Heb 9:17 Establishes that a covenant becomes binding at the death of the covenant-maker. Heb 9:22 Apart from the shedding of blood there is no remission. Heb 9:17 refers to the symbolic representation of the death of the covenant-maker as a necessary step in the establishment of a covenantal relationship. Heb 9:18 continues the reference to the covenant-making ceremony by adding that the first covenant was not radified without blood.
In conclusion, through the sacrificial death of Christ, the Father accomplishes both the inauguration and the radification of the new covenant which is superior to the old (first) covenant established by the death of bulls and goats. Thereby accomplishing and securing eternal redemption for those of the old and the new covenant. The covenant people of God are found in Christ alone.