After the death of Jesus, we find that the first covenant made with Israel came to an end and was replaced with a New Covenant that would be unlike the old one. It's not an amendment or continuation of the Old Covenant. The writer of Hebrews stated the law from the first covenant was weak and useless and could make nothing perfect. The New would be a better covenant established upon better promises. Why? Because this time God wasn't going to make the covenant with us (the people), but rather with Himself so that it could not fail. Our participation in this new way is to simply believe.
Just for kicks - Something we mentioned during the podcast:
When we focus on our struggles and problems instead of the answer to them, it can be a frustrating endeavor. Jesus came to release the Israelites from a covenant that kept them in a constant state of sin consciousness. His one-time sacrifice was meant to put an end to this. If we're stuck in a mindset that revolves around trying to avoid sin with the commands of "thou shall not," it will generally cause an increase in sin, resulting in self-condemnation. The alternative is giving up and surrendering to the completed work of Jesus Christ.
Under the law, the Jewish people were trapped in a consciousness of sin because they were in a covenant based upon their works and repeated sacrifices that constantly brought a reminder of sins. In contrast, Christ offered one sacrifice for all time to remove the struggle of a guilty conscience and the taking away of sin to be remembered no more. We shouldn't be seeking freedom from sin, but begin realizing God already provided it through the blood of Jesus. We can now live in this freedom found in Him.