The “New Covenant” that is always mentioned is in reference to a quote from Jeremiah 31:13-33 which says:
“The days are coming,” declares the Lord, “when I will make a new covenant with the people of Israel and with the people of Judah. It will not be like the covenant I made with their ancestors when I took them by the hand to lead them out of Egypt, because they broke my covenant, though I was a husband to them declares the Lord. “This is the covenant I will make with the people of Israel after that time,” declares the Lord. “I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people."
With whom does God say the “New Covenant” is being made with? With the Jewish people. Whom did Jesus say he came for? “I have come only for the lost sheep of Israel” (Matthew 15:24). Paul said that “The Gospel is to the Jew first, and then to the Gentile” (Romans 1:6).
The Gentiles have been grafted in because of the Jewish people’s unbelief in Jesus as their Messiah. Romans 1:1,11 - “I ask then: Did God reject his people? By no means!..Again I ask: Did they stumble so as to fall beyond recovery? Not at all! Rather, because of their transgression, salvation has come to the Gentiles.”
And Paul continues to say about this same subject: “If some of the branches have been broken off, and you, though a wild olive shoot, have been grafted in among the others and now share in the nourishing sap from the olive root, do not consider yourself to be superior to those other branches.” So we (the church) have not taken the place of the Jewish people–in the sense that God has discarded them, nor have we become superior to them. We have been brought in to know their God, who is now our God also.
The Church teaches (because this is what the scripture teaches) that the Jewish people will eventually be brought back into the fold and will come to believe in the same Messiah that the Church now believes in.
"This is what the Lord says, he who appoints the sun to shine by day, who decrees the moon and stars to shine by night, who stirs up the sea so that the waves roar – the Lord Almighty is his name: “Only if these decrees vanish from my sight,” declares the Lord, “will the descendants of Israel ever cease to be a nation before me.” This is what the Lord says: “Only if the heavens above can be measured and the foundations of the earth below be searched out will I reject all the descendants of Israel because of all they have done,” declares the Lord. (Jeremiah 31:35-37)