By so much was Jesus made a surety of a better testament. And they truly were many priests, because they were not suffered to continue by reason of death:  But this man, because he continueth ever, hath an unchangeable priesthood. Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.


For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens; Who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people's: for this he did once, when he offered up himself. For the law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated for evermore. (HEBREWS 7:22-28)


For every high priest is ordained to offer gifts and sacrifices: wherefore it is of necessity that this man have somewhat also to offer... But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. (HEBREWS 8:3-6)





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. (HEBREWS 9:15)


 



 



For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people: And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away. - (HEBREWS 8:10-13)



But this [shall be] the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. - (JEREMIAH 31:33)