Paul describes Jews as "natural branches" (Rom. 11:24):
For if you were cut off from what is by nature a wild olive tree, and grafted, contrary to nature, into a cultivated olive tree, how much more will these natural branches be grafted back into their own olive tree?
He also said in vss. 11-12:
I ask then, they did not stumble into an irrevocable fall, did they? Absolutely not! But by their transgression salvation has come to the Gentiles, to make Israel jealous. Now if their transgression means riches for the world and their defeat means riches for the Gentiles, how much more will their full restoration bring?
After vs. 24, he goes on:
For I do not want you to be ignorant of this mystery, brothers and sisters, so that you may not be conceited: A partial hardening has happened to Israel until the full number of the Gentiles has come in. And so all Israel will be saved, as it is written:
“The Deliverer will come out of Zion;
he will remove ungodliness from Jacob.
And this is my covenant with them,
when I take away their sins.”
In regard to the gospel they are enemies for your sake, but in regard to election they are dearly loved
for the sake of the fathers. For the gifts and the call of God are irrevocable.
An individual's salvation is always based on his faith and repentance. (But even in the NT, there are corporate aspects as well as individual: for example, the election of NT believers is primarily corporate: the church as the body of Christ is elect, and individuals become elect by being in Christ). The election or calling of Israel does not guarantee anyone's salvation or their place in the kingdom; they must believe in the Redeemer just like the rest of us. God chose Israel as a nation for service: not superior to other nations, but to mediate blessings to the nations (the Redeemer and the Scriptures), and to be a model or microcosm of what God would do for all nations in the kingdom. And as Paul says, God is still holding out His hands to Israel, even though they are currently His enemies, and anticipates their eventual inclusion and more blessings to the world through that.
This agrees with Jeremiah, who said in chapter 31,
“Indeed, a time is coming,” says the Lord, “when I will make a new covenant with the people of Israel and Judah. It will not be like the old covenant that I made with their ancestors when I delivered them from Egypt. For they violated that covenant, even though I was like a faithful husband to them,” says the Lord. “But I will make a new covenant with the whole nation of Israel after I plant them back in the land,” says the Lord. “I will put my law within them and write it on their hearts and minds. I will be their God and they will be my people.
...
The Lord has made a promise to Israel. He promises it as the one who fixed the sun to give light by day and the moon and stars to give light by night. He promises it as the one who stirs up the sea so that its waves roll. His name is the Lord of Heaven’s Armies. The Lord affirms, “The descendants of Israel will not cease forever to be a nation in my sight. That could only happen if the fixed ordering of the heavenly lights were to cease to operate before me.” The Lord says, “I will not reject all the descendants of Israel because of all that they have done. That could only happen if the heavens above could be measured or the foundations of the earth below could all be explored,” says the Lord.
As far as I'm aware, the sun and moon are still up there. Paul and Jeremiah, therefore, argue for the continued validity of the promises to Israel under the Abrahamic Covenant. The covenant with Abraham set the overarching framework by which salvation came. Both the Old Covenant (Mosaic Covenant), and the New Covenant were made in/under the framework provided by the Abrahamic Covenant. The promises made to Abraham and David are being fulfilled in the New Covenant, and all will be completely fulfilled (including some of the New Covenant conditions mentioned by Jeremiah) in the millennial kingdom.
We have new and expanded revelation that Gentiles no longer have to become Jews (proselytes) and keep the OT law to become saved, but God has provided a new body where the middle wall of partition has been broken down. But this is progressive revelation, and it expands or adds to previous revelation, rather than changing or contradicting it. The OT always taught the salvation of Gentiles along with Jews in the kingdom of God; the NT gives us more information about that.
The Mosaic Covenant (the Law) has been fulfilled in Christ. This is the covenant that has been made obsolete (Heb. 8:13) and replaced by something better, i.e. the New Covenant. Consequently, Christians are not under the Old Testament Law, and should teach and interpret it entirely only in light of its fulfillment. Christians are under the Law of Christ, i.e. New Testament teachings, and are to live by the power of the Spirit rather than the letter of the law (but if we fail to walk with the Spirit, we need law to correct us). Note that this emphasizes discontinuity between the OT and NT, contrary to Reformed thinking.