When Jesus instituted what we call the Lord’s Supper, He pointed to the cup that points to His covenant.
After telling His disciples to eat the bread representing His body, “he took a cup, and when he had given thanks he gave it to them, saying, ‘Drink of it, all of you, for this is my blood of the covenant, which is poured out for many for forgiveness of sins'” (Matthew 26:27-28). Luke recorded it also, “Likewise the cup after they had eaten, saying, ‘This cup that is poured out for you is the new covenant in my blood'” (Luke 22:20).
The “new covenant” is named as such in Jeremiah 31:31, and related descriptions are paralleled in Ezekiel 36. This new covenant is not like the Mosaic covenant given to Israel when they came out of Egypt. In this one, the Lord promised to put His law directly within them, to write it not on stone tablets but on their hearts. This covenant wouldn’t just point out why they needed forgiveness, it would purchase and apply it.
In its original setting the new covenant was for “the house of Israel and the house of Judah” (Jeremiah 31:31). The Lord compared the likelihood that He would fulfill this promise to the fixed order of the sun and moon. “If this fixed order departs from before me, declares the LORD, then shall the offspring of Israel cease from being a nation forever” (Jeremiah 31:35-36).
And it is the Lord who has opened the door for us who were not Jews to enjoy the good news of forgiveness and new hearts. He has opened the way for us, He will finish His promise to save a coming generation of Israel by His Spirit (Romans 11:25-26), and His Word is as good as it has ever been.