No, as I said, one contains the other. A will ("testament") contains promises ("covenants"). A new will with its promises and devises revokes the old will and its promises.
The new testament with its new covenant ("better promises" (Heb 8:6)) has replaced and revoked the old testament and its promises. In your scenario, the old covenant has been revoked with nothing. It doesn't work like that with God or man. God has revoked the old covenant by bringing in a better (new) covenant. "In that he says, a new covenant, he has made the first old" (Heb 8:13).
You are minimizing the impact of the cross on this Easter Sunday. Jesus' perfect sacrifice on the cross changed EVERYTHING. We are no longer under the law of the old covenant, we are under the grace of the new covenant.
The essence of the new covenant is God promising, "I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more" (Heb. 8:12). That is NOW my friend becasue of the perfect sacrifice of Jesus Christ by which we receive the gift of righteousness (Rom 5:17) and become the righteousness of God (2 Cor 5:21). He has truly been merciful to our unrighteous and our sins and iniquities he no longer remembers. Otherwise how is it that we are "made the righteousness of God" (2 Cor 5:21) and "as He is, so are we in this world" (1 John 4:17)? Does God see any sin in Jesus? Of course not. Neither does he see any sin in you becasue as He is so are we in this world. That's proof of the efficacy of the new covenant that "our sins and iniquities He no longer remembers."
"It is finished" is a powerful statement by our Lord. The old covenant is finished and we are under the new. Don't let anyone try to tell you that because grace, the new covenant, and the new testament are no the same thing that they are somehow not effective. That's Satan's lie. Grace (unmerited favor) is the essence of the promise of the new covenant contained in the new testament. Jesus' long awaited and perfect sacrifice on the cross put all into effect and ALL THINGS ARE BECOME NEW for those of us in Christ (2 Cor 5:17).
God's word is deep and always multilevel. We are the spiritual Jews who enjoy these promises now. Soon a remnant of Israel in the flesh will also enter into these promises as well. Both spiritual and natural Jews will live in these promises throughout the millennium and forever. Neither excludes the other.
Our Bibles contain the Old and New TESTAMENTS, not Old and New Covenants.
The New Covenant is a specific promise made to Israel.
It is established by the New Testament Blood atonement.
What was made 'old' in Heb 8 was the Mosaic Law, which could not save.
The New Covenant replaces the requirement that the Jew was under while under the Mosiac Law, so he will not be under that Law in the Millennium.
Hbr 8:11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
Hbr 8:12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.
That is not for today, that is for the Millennium. No one is told today not to teach about the Lord. All of the chapter has to read as one promise, not just particular verses.
It isn't for today, it is for the Jew who is saved and enters into the Millennium Kingdom.