Hebrews 7-9 deals with the old law/new law in depth.
11 If perfection could have been attained through the Levitical priesthood—and indeed the law given to the people established that priesthood—why was there still need for another priest to come, one in the order of Melchizedek, not in the order of Aaron?
13 He of whom these things are said belonged to a different tribe, and no one from that tribe has ever served at the altar. 14 For it is clear that our Lord descended from Judah, and in regard to that tribe Moses said nothing about priests. 15 And what we have said is even more clear if another priest like Melchizedek appears, 16 one who has become a priest not on the basis of a regulation as to his ancestry but on the basis of the power of an indestructible life.
18 The former regulation is set aside because it was weak and useless 19 (for the law made nothing perfect), and a better hope is introduced, by which we draw near to God.
22 Because of this oath, Jesus has become the guarantor of a better covenant.
23 Now there have been many of those priests, since death prevented them from continuing in office; 24 but because Jesus lives forever, he has a permanent priesthood. 25 Therefore he is able to save completely[
c] those who come to God through him, because he always lives to intercede for them.
28 For the law appoints as high priests men in all their weakness; but the oath, which came after the law, appointed the Son, who has been made perfect forever.
8 Now the main point of what we are saying is this: We do have such a high priest, who sat down at the right hand of the throne of the Majesty in heaven, 2 and who serves in the sanctuary, the true tabernacle set up by the Lord, not by a mere human being.
7 For if there had been nothing wrong with that first covenant, no place would have been sought for another. 8 But God found fault with the people and said[
b]:
“The days are coming, declares the Lord,
when I will make a new covenant
with the people of Israel
and with the people of Judah.
9 It will not be like the covenant
I made with their ancestors
when I took them by the hand
to lead them out of Egypt,
because they did not remain faithful to my covenant,
and I turned away from them,
declares the Lord.
10 This is the covenant I will establish with the people of Israel
after that time, declares the Lord.
I will put my laws in their minds
and write them on their hearts.
I will be their God,
and they will be my people.
11 No longer will they teach their neighbor,
or say to one another, ‘Know the Lord,’
because they will all know me,
from the least of them to the greatest.
12 For I will forgive their wickedness
and will remember their sins no more.”[
c]
13 By calling this covenant “new,” he has made the first one obsolete; and what is obsolete and outdated will soon disappear.