The remedy for sin is the same, whether it be for the sinner who has not trusted Christ; or for the Believer who has trusted Christ for salvation, but is in a sinful state. The remedy is the Gospel. Humanity ties to work themselves back into favor with God by trying to do good works. The Believer tries the same.
However, when the Believer sins (and he or she will) the most important, and only thing to do is to BELIEVE THE GOSPEL! When we look at the work of Christ, we are looking into his mercy, grace and love. This alone is the only way to have true peace with God.
After pointing out the eternal promises of the Heavenly City compared with the current persecution, even martyrdom of the saints, and those before, the writer of Hebrews states:
Wherefore seeing we also are compassed about with so great a cloud of witnesses, let us lay aside every weight, and the sin which doth so easily beset us, and let us run with patience the race that is set before us, Looking unto Jesus the author and finisher of our faith; who for the joy that was set before him endured the cross, despising the shame, and is set down at the right hand of the throne of God. For consider him that endured such contradiction of sinners against himself, lest ye be wearied and faint in your minds. (Hebrews 12:1-3)
Let us lay aside the weight, and look to Jesus!