Old Covenant (Testament)

Gen 17:10-11
This is My covenant which you shall keep, between Me and you and your descendants after you: Every male child among you shall be circumcised; 11 and you shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between Me and you.
NKJV

Ex 24:7-8
Then he took the Book of the Covenant and read in the hearing of the people. And they said, "All that the LORD has said we will do, and be obedient." 8 And Moses took the blood, sprinkled it on the people, and said, "This is the blood of the covenant which the LORD has made with you according to all these words."
NKJV

2 Cor 3:2-6
You are our epistle written in our hearts, known and read by all men; 3 clearly you are an epistle of Christ, ministered by us, written not with ink but by the Spirit of the living God, not on tablets of stone but on tablets of flesh, that is, of the heart. 4 And we have such trust through Christ toward God. 5 Not that we are sufficient of ourselves to think of anything as being from ourselves, but our sufficiency is from God, 6 who also made us sufficient as ministers of the new covenant, not of the letter but of the Spirit; for the letter kills, but the Spirit gives life.
NKJV

Gal 3:19
What, then, was the purpose of the law? It was added because of transgressions until the Seed to whom the promise referred had come. The law was put into effect through angels by a mediator.
NIV

Gal 3:24-25
Therefore the law was our tutor to bring us to Christ, that we might be justified by faith. 25 But after faith has come, we are no longer under a tutor.
NKJV

1 Tim 1:8-10
We know that the law is good if one uses it properly. 9 We also know that law is made not for the righteous but for lawbreakers and rebels, the ungodly and sinful, the unholy and irreligious; for those who kill their fathers or mothers, for murderers, 10 for adulterers and perverts, for slave traders and liars and perjurers-and for whatever else is contrary to the sound doctrine
NIV

Heb 8:7-8
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:
NIV

Heb 8:13
In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away.
NKJV

Heb 10:4
For it is not possible that the blood of bulls and goats could take away sins.
NKJV

First there was the covenant that Yahweh made with Abraham. The fulfillment of that covenant would not come to pass until the Messiah came. Then God established Israel as his chosen people. God gave Moses the Torah (Law) as a guide so that they would not sin against him. The purpose of this was to "lead" the people to the Messiah.
Some people believe that the Old covenant is no longer relevant. But yet we find it quoted so much in the New testament.

What was wrong with the first covenant? Take note in Hebrews 8:8 that the problem was not the covenant itself, it was with the people. He took away the daily sacrifice and provided the sacrifice himself.

Gen 22:8
"God himself will provide the lamb for the burnt offering, my son."
NIV