The first question to answer is which 'Old' Covenant'?
There are at least five covenants in the Bible between God and human beings, usually the Noaic, Abrahamic, Mosaic, Davidic and the New Covenants, and possibly more. We might assume that by the 'Old' covenant we really mean the Mosaic one, since this relates to the giving of the Law/Torah. We find New Testament passages explaining clearly enough that its jurisdiction over believers in Christ does not remain after we have received Christ. Even that understanding though still leaves another four more 'Old' covenants in place.
These covenants are also interwoven historically and narratively. With Noah we have the institution of a basic moral code and God's commitment to the redemption of all humankind. The Abrahamic constitutes God's people and gives them a land, the Mosaic remembers that people and instructs specifically how they should live in that land, the Davidic then assures an eternal Kingdom for the people, in the land overseeing God's instruction from the line of David (often interpreted as a 'Messiah'), then we have Jesus born in David's line to establish said Kingdom.
So to my mind we reflect Scripture far better to speak of the 'Old' and 'New' covenants confirming and ratifying one another, not of the 'Old' covenant ending. We are after all doing theology here, and the reason we can debate this is because the Scriptures don't speak directly in these exact terms. We are offering interpretation.
In Hebrew, the word 'Berith', or Covenant, is indicative of an eternal and unconditional relationship - I can provide follow up examples to back this up if anyone is interested. When God makes a covenant, therefore, it doesn't end. The relationship and promises remain in place forever, incorporated into anything that follows. A covenant is different from a contract, which is a conditional relationship. With a contract, promises and benefits depend strictly on the involved parties abiding by certain conditions. A contract makes provision for it breaking. A covenant does not.
Suggesting the Old Covenant ended involves turning a covenant into a contract. I would argue that when God makes a covenant, that's irrevocable. Again, I can say loads more addressing possible objections that covenants surely have to still be conditional.
The direct implications of this for us if accepted would be: 1) The continued place of the Jewish people as God's people as well as a positive assessment both of Jewish faith-practice and the importance of a home in Israel. 2) The church being fully grafted in and sharing that Israel-status with them (we are fully Torah observant 'in Christ', who kept the Law on our behalf). This also gives us irrevocable assurance of our Salvation in Christ once received, and the universality of God's calling to receive that gift of salvation (though not necessarily that all will receive it).
Would love to hear if that resonates with anybody.