The question of the covenants has been greatly distorted and misunderstood. Briefly let us notice what the old covenant was not. It was not the Ten Commandments. Why? Because they did not wax old and vanish away (verse 13). They did not have poor promises (verse 6) and they were not faulty (verse 7).
Then what was the old covenant, and how was it ratified? It was an agreement between God and Israel described in Exodus 19:5-8 whereby the people promised to keep the Ten Commandments. It was ratified by the sprinkled blood of an ox (Exodus 24:7, 8). The poor promises of the people failed because they tried to obey in human strength alone.
In comparison, the new covenant was instituted and ratified by the blood of Jesus at His death (Hebrews 12:24; 13:20; Matthew 26:28). It went into effect when He died. "For a testament [covenant] is of force after men are dead: otherwise it is of no strength at all while the testator liveth." Hebrews 9:17.
Now get this point also about the new covenant: "Though it be but a man's covenant, yet if it be confirmed, no man disannuleth, or addeth thereto." Galatians 3:15. This means that after the death of Christ, nothing could be added to or taken away from the new covenant. This is why Jesus introduced the Lord's Supper on Thursday night before He died--so that it would come under the new covenant (Matthew 26:28).
But ponder this question, and don't miss the significance of it. When did Sundaykeeping begin? All will answer, "After the resurrection of Jesus." Then it could not be a part of the new covenant. Nothing could be added after the death of Jesus, the Testator.