(Hebrews 8:13)…..In that He says, “A new covenant,” He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away. The part of the Bible we call the Old Testament is not exactly the same as the Old Covenant, nor is the part of the Bible we call the New Testament exactly the same as the New Covenant. The Old Covenant was an agreement between God and the children of Israel. We have the record of it in the Old Testament. The New Covenant is an agreement between God and Jesus Christ. (Therefore it includes all who are united with Jesus Christ, or as the Bible says, all those who are “in Christ.”
The New Testament is the name we give to the 27 books of the Bible from Matthew through Revelation. The New Testament book is not the New Covenant, but reveals it and explains it. The New Covenant did not start until after the death of Jesus Christ. For it was sealed by the precious blood of Jesus paying the price for the complete remission of sins for all who believe in Him. Jesus himself plainly said the New Covenant involved His blood being shed. (Matthew 26:28) “For this is My blood of the new covenant, which is shed for many for the remission of sins.
The following passage in Hebrews also makes clear that the New Covenant could not begin until after the death of Jesus Christ.
(Hebrews 9:14-17 NASB)…..how much more will the blood of Christ, who through the eternal Spirit offered Himself without blemish to God, cleanse your conscience from dead works to serve the living God? 15 And for this reason He is the mediator of a new covenant, in order that since a death has taken place for the redemption of the transgressions that were committed under the first covenant, those who have been called may receive the promise of the eternal inheritance. 16 For where a covenant is, there must of necessity be the death of the one who made it. 17 For a covenant is valid only when men are dead, for it is never in force while the one who made it lives.
Why does it matter when the New Covenant started? Because it is the key to rightly dividing the Word of God, which (2 Timothy 2:15) reveals is necessary. Without a clear understanding of when the New Covenant starts, and what the New Covenant is, we will be confused. (Not understanding this clearly is why so many teach different things about what is required to be in good standing with God.)
The entire earthly ministry of Jesus happened under the Old Covenant and was directed only to Israel (Matthew 15:24, Romans 15:8). When Jesus first sent out His disciples He told them to only go to the people of Israel (Matthew 10:5-6). But after His resurrection they were sent into all the world to tell the Good News to everyone.