15 But the Holy Spirit also witnesses to us; for after He had said before,
16 “This is the covenant that I will make with them after those days, says the LORD: I will put My laws into their hearts, and in their minds I will write them,”
17 then He adds, “Their sins and their lawless deeds I will remember no more.”
18 Now where there is remission of these, there is no longer an offering for sin.
The quote in verses 16-17 is from Jeremiah 31:33-34 (as in Hebrews 8:8-12).
Jeremiah wrote the words, but the Holy Spirit is the author.
So, to continue to offer sacrifices is, for the Jew, a rejection of their own prophet Jeremiah and of the Holy Spirit.
The New Testament saint has both the advantages of regeneration and the personal indwelling and the sanctifying work of the Holy Spirit. Thus, under the First Testament God wrote His laws on stone, whereas under the New Testament He writes them upon the heart.
The other distinctive feature of the New Testament is the fact that God remembers sins and iniquities no more. The constant repetition of the sacrifices demonstrated that the sin question was not settled. The once for all offering of the Messiah shows that sin is paid for and put away. — Hebrews in the Greek New Testament, by Kenneth S. Wuest, page 177