If that Old Covenant couldn't get the job of Salvation done, then it was time to get rid of It, making the needed change. The "better hope" is by 'faith', and is the hope of our Salvation through Christ Jesus The Son of God, now our High Priest to The Father for us.

Heb.7:20    And inasmuch as not without an oath He was made Priest:
21    (For those priests were made without an oath; but This with an oath by Him That said unto Him, "The LORD sware and will not repent, Thou art a Priest for ever after the order of Melchisedec:)
22    By so much was Jesus made a surety of a better testament.

     Abraham understood the later need, for "a better testament" (Covenant), as he believed on the Promise of Salvation through Christ Jesus, and God counted it to him as righteousness.

Heb.7:23    And they truly were many priests, because they were not suffered to continue by reason of death:
24    But this Man, because He continueth ever, hath an unchangeable priesthood.
25    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.

     Even the sons of Aaron and those of the Levitical priesthood eventually died, ending each one of ther offices as priest. But our Lord Jesus Christ continued His Office as High Priest, by His resurrection to the right hand of The Father. None other than The Lord Jesus Christ had The Power and Authority to continue That Office of High Priest after death. Since He lives, He only is able to reconcile us to The Father through His Blood.

Heb.7:26      For such an High Priest became us, Who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens;
27    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.
28    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.

The New Covenant:  A Better Testament Given

     This "oath", which was 430 years before The Law, was That Promise to Abraham that through his seed, all families of the earth would be blessed in the Salvation through our High Priest forever after the order of Melchizedek, Which is God's Savior Jesus Christ, The New Covenant (Testament). (See also Psalms 110; Psalms 89:34-37). How could we ever be saved by that Old Covenant, as those sacrifices never redeemed anyone from bondage of the 'law of sin'? Righteous Abraham knew the answer even then:

Matt 26:26    And as they were eating, Jesus took bread, and blessed it, and brake it, and gave it to the disciples, and said, "Take, eat; this is My body."
27    And He took the cup, and gave thanks, and gave it to them, saying, "Drink ye all of it;
28    For this is My blood of the new testament, which is shed for many for the remission of sins."

     Our Lord Jesus in His Role as 'High Priest' was this Melchizedek (King of Righteousness), and He offered Abraham Holy Communion with Him (Gen.14). That time with Abraham was the first act of Holy Communion with Christ, and it was by 'faith' on our Lord Jesus as God's Savior 'Immanuel' Who would come. So finally, we now have a Perfect Sacrifice by Blood, of The Testator of a New Covenant, in Jesus Christ Yeshu'a Messiah, a Perfect Covenant not of the flesh, not of circumcision of the flesh, not of imperfect priestly ordinances of ritual and animal sacrifice, not of religious dogma, but... of 'faith' by His Spirit dwelling in us.