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: