Who is the New Covenant made with in Jeremiah 31?

Jeremiah 31:31 states God will make a new covenant with the house of Israel and with the house of Judah. The context emphasizes it is made with Israel, and no one but Israel. Believers in the Age of Grace enjoy its benefits but are not themselves in that covenant relationship; they are members of the Body of Christ.

Les teaches from Jeremiah 31:31 that the new covenant is made with the house of Israel and with the house of Judah. He notes that many theologians claim believers in the Age of Grace are under the New Covenant, but reading the Bible in plain English, that cannot fly, because God makes this New Covenant with Israel and no one but. Les explains that while we are not in a covenant relationship, we enjoy the benefits of everything God did to fulfill this covenant with Israel: the work of the cross, the power of His resurrection, the coming of the Holy Spirit, and the blessings of this Age of Grace. We are members of the Body of Christ, He is the Head, and we are in the Body, but not in a covenant relationship.

Jeremiah 31:31

Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:

What is the new covenant promised in Jeremiah 31:31?

God promises to make a new covenant with the house of Israel, not like the old covenant of law. Under it, no one will need to be taught the Word of God, every Israelite will have God's heart within them, be an obedient people of faith, be cleansed from all iniquity, and prosper materially.