The short answer is yes, it certainly will be built. When Jesus Christ returns to judge this world, he will restore the kingdom of Israel as the kingdom of God. He will reign over the mortal population of the earth for 1000 years.
His throne will be the restored throne of David in Jerusalem.
Luke 1:31 And now, you will conceive in your womb and bear a son, and you will name him Jesus. 32 He will be great, and will be called the Son of the Most High, and the Lord God will give to him the throne of his ancestor David. 33 He will reign over the house of Jacob forever, and of his kingdom there will be no end."
When he returns to the mount of Olives (from which he ascended), a great earthquake will change the topography of the land of Israel.
Zechariah 14:4 And in that day His feet will stand on the Mount of Olives, Which faces Jerusalem on the east. And the Mount of Olives shall be split in two, From east to west, Making a very large valley; Half of the mountain shall move toward the north And half of it toward the south. 5 Then you shall flee through My mountain valley, For the mountain valley shall reach to Azal. Yes, you shall flee As you fled from the earthquake In the days of Uzziah king of Judah. Thus the LORD my God will come, And all the saints with You. 6 It shall come to pass in that day That there will be no light; The lights will diminish. 7 It shall be one day Which is known to the LORD—Neither day nor night. But at evening time it shall happen That it will be light.8 And in that day it shall be That living waters shall flow from Jerusalem, Half of them toward the eastern sea And half of them toward the western sea; In both summer and winter it shall occur. 9 And the LORD shall be King over all the earth. In that day it shall be—"The LORD is one," And His name one. 10 All the land shall be turned into a plain from Geba to Rimmon south of Jerusalem. Jerusalem shall be raised up and inhabited in her place from Benjamin’s Gate to the place of the First Gate and the Corner Gate, and from the Tower of Hananeel to the king’s winepresses. 11 The people shall dwell in it; And no longer shall there be utter destruction, But Jerusalem shall be safely inhabited.
Jerusalem will be rebuilt with a sanctuary and temple to the north as described by Ezekiel.
The prophecy of Psalm 2 will be fulfilled
Psalm 2:1 Why do the nations rage, And the people plot a vain thing? 2 The kings of the earth set themselves, And the rulers take counsel together, Against the LORD and against His Anointed, saying, 3 Let us break Their bonds in pieces And cast away Their cords from us." 4 He who sits in the heavens shall laugh; The Lord shall hold them in derision. 5 Then He shall speak to them in His wrath, And distress them in His deep displeasure: 6 "Yet I have set My King On My holy hill of Zion. 7 I will declare the decree: The LORD has said to Me, ‘You are My Son, Today I have begotten You. 8 Ask of Me, and I will give You The nations for Your inheritance, And the ends of the earth for Your possession. 9 You shall break them with a rod of iron; You shall dash them to pieces like a potter’s vessel.’10 Now therefore, be wise, O kings; Be instructed, you judges of the earth. 11 Serve the LORD with fear, And rejoice with trembling. 12 Kiss the Son, lest He be angry, And you perish in the way, When His wrath is kindled but a little. Blessed are all those who put their trust in Him.
The prophecy of Isaiah 2 will be fulfilled
Isaiah 2:1 The word that Isaiah the son of Amoz saw concerning Judah and Jerusalem. 2 Now it shall come to pass in the latter days That the mountain of the LORD’S house Shall be established on the top of the mountains, And shall be exalted above the hills; And all nations shall flow to it. 3 Many people shall come and say, "Come, and let us go up to the mountain of the LORD, To the house of the God of Jacob; He will teach us His ways, And we shall walk in His paths." For out of Zion shall go forth the law, And the word of the LORD from Jerusalem. 4 He shall judge between the nations, And rebuke many people; They shall beat their swords into plowshares, And their spears into pruning hooks; Nation shall not lift up sword against nation, Neither shall they learn war anymore.
Perhaps the hardest thing for us to understand is that animal sacrifices will be instituted again for the mortal population.
This is described in Ezekiel.
It is not too difficult to understand why.
Before Christ gave his life as a sacrifice for sin, the animal sacrifices pointed forward to his sacrifice.
In the kingdom of God, the animal sacrifices will serve as a reminder to the mortal population that Jesus sacrificed his life so that their sins might be forgiven.
The sacrifices also provide food for the priests and those making the sacrifices.
I hope you find this helpful.