The New Testament is not the New Covenant. To make the New Testament equal to the New Covenant is to deny God’s promises to Israel. When Balaam, with Balak’s encouragement, attempted to undermine God’s promises to Israel, God told him, “God is not man that he should lie; neither the son of man that he should repent: hath he said, and shall he not do it? or hath he spoken, and shall he not make it good?” Any hermeneutic that argues that God will go back on His literal promises to Israel is a hermeneutic that starts by calling God a liar. Rather, “…let God be true and every man a liar.”
None of the New Testament Scriptures indicate that God will fail to fulfill His promises in the Old Testament covenants. In fact the New Testament writers quote the Old Testament Scriptures as words of God not to be questioned. What God has promised He will do. And He will do it exactly as He has promised it.
God has said specifically that He will establish the new covenant with Israel. Paul says He will do that when the Deliverer will return to Israel. That obviously has not happened yet. Jesus instituted the new testament in His blood at His crucifixion. That has happened. The new testament and the new covenant are quite different. It is confusing that Greek New Testament Scriptures cannot distinguish these two concepts by different Greek words. But God has refined His words according to Psalm 12:6. Those refined words preserved for us in the King James Version have sorted out these concepts for us, so we can easily see how all of God’s promises to Israel will be fulfilled without modification.
Tribulation saints will be on earth after the Church has gone to heaven and before the new covenant is instituted at the start of the Kingdom. The discussion of the already established new testament and the coming new covenant in the Epistle to the Hebrews will be especially useful to them. They will need the information there about salvation and covenants to know how to live for God at that time.
See slides: The New Testament is not the New Covenant for a Scriptural explanation of these things.