In Hebrews 10:20 we are told that this New Covenant is "a new and living way." The truth in those words needs to ring in our hearts, expand our revelation, and direct our walk. Everything in this New Covenant is new. In Christ Jesus, we are a new creation (II Corinthians 5:17). None of the old creation was brought over. The promises of the New are better than the Old (Hebrews 8:6). The promises on which the New Covenant is based are the Savior and the Holy Spirit. Both are God himself, and both have been given. This makes the foundation as sure as God Himself. This covenant cannot fail because it is a covenant in the life of God. "It is God who works in you both to will and to do for His good pleasure" (Philippians 2:13). No wonder Paul could say, "I can do all things through Christ who strengthens me" (Philippians 4:13).
The Old Covenant depended on what man could do. It failed because man apart from God lacks the ability to meet the standards of a Holy God. The New Covenant will not fail because it depends alone on what God can do. Man does have a part, but it is not to help God. It is not a "50-50" relationship. It is a "100-100" relationship. Man submits to God in faith without reservation, and the full power of God is manifested without limit in vessels of clay. Glory! Even the changing that takes place in these earthen vessels is not from defeat to victory, but "from glory to glory" (II Corinthians 3:18). "But we have this treasure in earthen vessels, that the excellence of the power may be of God and not of us" (II Corinthians 4:7)
One of the promises in this New Covenant is that God will put His laws in our minds and write them on our hearts (Hebrews 8:10). The commandments of the old Law were written on tablets of stone. Men memorized them, and tried to obey. They taught their children saying, "Know the Lord." Now the old has passed away! We do not know God in that way any longer. He has given us His life that we may know Him in reality. "And this is eternal life, that they may know You, the only true God, and Jesus Christ whom You have sent" (John 17:3). "But the hour is coming, and now is, when the true worshipers will worship the Father in Spirit and truth; for the Father is seeking such to worship Him. God is Spirit, and those who worship Him must worship in Spirit and truth" (John 4:23,24).
We do not know God in an intellectual way with our minds. We still have minds, and we need to set our minds on eternal things, but the mind is only a faculty of our being for certain purposes. Knowing God is a matter of the Spirit. Fellowship is in the Spirit, in the life of God, not in the mind. The mind is used to reason about many things. The mind may reason about food, but reasoning about food does not satisfy hunger or nourish the body. So it is with God. We may reason about the things of God, but nourishment only takes place as we experience God in the Spirit and eat of the living bread. "Man shall not live by bread alone, but by every word that proceeds from the mouth of God" (Matt. 4:4).
The living word is what the Holy Spirit writes on our hearts and minds. Our focus is on our relationship with God by the Spirit. This is an entirely new working in the New Covenant that the saints in the Old knew nothing of, and it takes everything out of the dead letter and into life. Search the New Testament from cover to cover and see how God has lifted His entire working out of the dead letter, from commandments written in stone--to life, with His word being written in our hearts and minds by the Spirit.