A Better Priesthood

The book of Hebrews is about the distinction between the Old and New Covenants:
For there is truly a disannulling of the commandment going before for the weakness and unprofitableness thereof. For the law made nothing perfect, but the bringing in of a better hope did; by the which we draw near to God. (Heb 7:18-19).

What was disannulled? Conditionality was disannulled and a dependence upon human performance. It was replaced with an oath and fulfilled in Christ alone.
For the law makes men high priests who have infirmity; but the word of the oath, which was since the law, makes the Son, who is consecrated forever more. (Heb 7:28).

Under the Old Covenant, the efficacy of Levi’s priesthood depended on Levi fulfilling the law himself, which he could not do. And when the Levitical priesthood failed, all the people suffered. Because the Old Covenant depended on the performance of man it was unprofitable and had to be laid aside.

For if the first covenant had been faultless, then should no place have been sought for the second. For finding fault with them, He said, Behold, the days come, says the Lord, when I will make a new covenant with the house of Israel and with the house of Judah. (Heb 8:7-8).

God must have a covenant which does not depend on human performance, the meeting of conditions. He had this in mind before He made the worlds. He allowed man to try first to see for himself whether he was able to meet all of the conditions and when man failed, He brought forth His Son.