If the Temple in Jerusalem is to be literally rebuilt in the future, then the close connection between the Temple and the Ark means that the Ark will be present then.
In Revelation 11:1-2 it states … go and measure the Temple of God and the altar….for 42 months the Gentiles will trample the Holy city underfoot.
Matthew 24:15 So when you see the ‘abomination of desolation’ of which Daniel spoke, standing in the Holy place… Daniel 9:27…he will put a stop to the sacrifice and offerings
Isaiah 60:13 the glory of Lebanon will come to you, to adorn His holy sanctuary, to honour the place where I stand.
Ezekiel 43:1-12…the Glory of the Lord came into the Temple by the East gate.
These, and other, texts make it clear that the Temple will exist again on the Temple mount, complete with reinstated rituals, until Return of Jesus and His Millennial reign. Isaiah 56:8
The original purpose for building a Temple was to house the Ark. This implies that that which is housed is greater than that which houses it. If so, then the return of the Ark is necessary for the rebuilt Temple.
It might be argued that since the Presence of God had departed from the Ark/Temple, then the Ark no longer retains its sanctity, and is no longer necessary. But, the Temple continued to have its spiritual significance for long after that happened. Along this line, it may also be argued that the consummating nature of Christ’s atonement for sin ended the need for the Ark’s mercy seat. Yet it is apparent that the temple had sanctity for Jesus during His life and continued to do so for the early Church.
The Ark awaits rediscovery, perhaps hidden under the Temple Mount, or at Mt Nebo; 2 Maccabees 2:4-8, then at that time, we will see the building of the Third Temple.
Haggai 2:6-9 These are the words of the Lord; In a little while from now, I shall shake the heavens, the earth and the sea. I shall shake all the nations and the treasure of all nations will come here and I shall fill this House with splendor. Mine is the silver and the gold – the splendor of this latter House will surpass that of the former. In this place I shall grant prosperity and peace.
Jeremiah 3:18 In those days Judah will be reunited with Israel, together they will come from the North into the Land that I gave to their forefathers.
Jeremiah 3:16-17 In those days, when you have increased and become fruitful in the Land, says the Lord, no one will speak any more of the Ark of the Covenant, remember it or resort to it. At that time, Jerusalem will be called the Throne of the Lord, and all the nations will gather to honour the Lords name. Jeremiah 50:4-5
“When you have increased and become fruitful” refers to the time when all the Lord’s faithful people, every Christian, are gathered into the Land of Greater Israel. After that, the Lord Jesus will return and commence His Millennial reign. Then the Ark will no longer be required. Ref; Randall Price