This clearly shows that G-d's mercy abounds to forgive sin because of the blood sacrifice of Yeshua. However, walking in the light of G-d, His Torah, is also necessary for fellowship to continue with Him. G-d's light is all the instruction that He has ever spoken. G-d's grace, on the other hand, is the very thing we need in order to perform that which is pleasing to Him, namely to obey His Law. Sha'ul did not mean that sin no longer mattered, or that grace would overlook sin.
Grace rules through righteousness.
So grace is the enablement to act out righteousness. The Law is no longer something pressing on us to showcase how unlawful we are. Rather, now grace is pressing on us to fill us with the righteous nature of G-d Himself. In such a case the Law is no longer a burden, but rather the usual result of being filled with the divine nature. It is the grace of G-d toward us that provides us with the New Covenant in Messiah Yeshua.