"Behold, the days are coming, declares the Lord, when I will fulfill the promise I made to the house of Israel and the house of Judah. In those days and at that time I will cause a righteous branch to spring up for David, and He shall execute justice and righteousness in the land. In those days Judah will be saved and Jerusalem will dwell securely. And this is the name by which it will be called: 'The Lord is our righteousness.' for thus says the Lord: David shall never lack a man to sit on the throne of the house of Israel, and the Levitical priests shall never lack a man in My presence to offer burnt offerings, to burn grain offerings, and to make sacrifices forever." (Jeremiah 33:14-18)
To my mind, this is an exhilarating passage, because it unites so many messianic themes. The Branch is an epithet used for the coming Messiah several times in Jeremiah, and points to the coming of Jesus, about 600 years after the historical events of the book. The prophet uses several confirmatory references that we know from the New Testament. First, the Branch will cause His people to bear the name "The Lord is our righteousness." This should cause any Christian to think immediately of the words of Paul in II Corinthians 5:21: "For our sake, He [the Father] made Him [Jesus] to be sin who knew no sin, so that, in Him, we might become the righteousness of God." Contrary to the claims of some dispensationalists, this proves that the future conversion of the Jews will occur on the same basis as the conversion of the Gentiles, by faith alone in Christ alone, so that His righteousness is imputed to the elect believer. There is no separate class of saved people among the Jews (Acts 15:11). They simply follow a different historical track to arrive at that same place.
Furthermore, Jeremiah tells us that the Branch will fulfill a dual role, to fill the throne of David forever. "Once for all I have sworn by My holiness; I will not lie to David. His offspring shall endure forever, his throne as long as the sun before Me. Like the moon it shall be established forever, a faithful witness in the skies" (Psalm 89:35-37). The other is that He will sustain the work of the Levitical priests. We know that Jesus was of the tribe of Judah, not of Levi. However, the Epistle to the Hebrews addresses that question by telling us that Jesus's priesthood is not according to Levi, but according to the pattern of Melchizedek. "The one of whom these things are spoken belonged to another tribe, from which no one has ever served at the altar. For it is evident that out Lord was descended from Judah, and in connection with that tribe Moses said nothing about priests. This becomes even more evident when another priest arises in the likeness of Melchizedek, who has become a priest, not on the basis of a legal requirement concerning bodily descent, but by the power of an indestructible life. For it is witnessed of Him, 'You are a priest forever after the order of Melchizedek'" (Hebrews 7:13-17, quoting from Psalm 110:4; see also Hebrews 4:14-5:10). Together we have the Priest-King prophesied by Zechariah: "Behold the man whose name is the Branch, for he shall branch out from his place, and he shall build the temple of the Lord.It is he who shall build the temple of the Lord and shall bear royal honor, and shall sit and rule on his throne. An there shall be a priest on his throne, and the counsel of peace shall be between them both" (Zechariah 6:1-13, using Josiah the high priest as a type).
There can be no doubt that that the restoration of Israel will come, not as the political event expected by dispensationalism, but as a Gospel event, founded upon Jesus Christ alone as savior. It won't be at the same time as Gentile believers, but it will be by exactly the same faith, atonement, and imputation of His righteousness alone.
