The new covenant gives us right standing with GOD. That isn't taken away when we are unfaithful for it is written:
If we endure, we will also reign with [him]; if we deny [him], he also will deny us; if we are unfaithful, he remains faithful, because he cannot deny himself. 2 Timothy 2:12-13
The new covenant guarantees forgiveness of sin. If we sin, GOD is faithful to his covenant (and is just because of the cross) for it is written:
If we assent to our sins, he is faithful and just, so that he will forgive us [our] sins and will cleanse us from all unrighteousness. 1 John 1:9
Therefore, let us make a habit of assenting to the accusations of our mind and conscience, for there is no condemnation in Christ, and the holy spirit will cleanse our mind and conscience and lead us into all truth.
Be in agreement with your adversary quickly, while you are in the way with him; lest at any time the adversary deliver you to the judge, and the judge deliver you to the officer, and you be cast into prison. Verily I say unto you, you shall by no means come out thence, until you hast paid the uttermost farthing. Matthew 5:25-26