The New Covenant does not end, because we all depend on Jesus to be saved. Jesus said, "I am the way, and the truth, and the life; no one comes to the Father but through Me." (John 14:6).
So whether we are church-age Christians, rapture-time Christians, or believers during the Tribulation, we are all saved from our sins by repenting and believing in Jesus and His atonement on the cross for us.
This holds true for Old Testament time believers as well. For believers during Old Testament times, they believed God's word as it was being revealed to them. Because of their faith in God, they were also saved.
"The Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, 'All the nations will be blessed in you.'" (Galatians 3:8)
And "Abraham believed God, and it was reckoned to him as righteousness." (Galatians 3:6)
"So then those who are of faith are blessed with Abraham, the believer." (Galatians 3:9)
Therefore, Christ is the door to heaven and everlasting life for people of the past, present and future.
God credited Abraham and Old Testament saints with righteousness. But Christ paid for all their sins retroactively.
Jesus also paid for our sins and the sins of those who are not yet born.
As for those who become believers during the millennial reign, they also need Jesus. They will not be perfect humans, because they will be descendants of survivors of the Tribulation. At that time, Jesus will be King and reign on earth. The world will know what it will be like for Jesus to be king.
The people at that time will still need to depend on Jesus to forgive them of their sins.
Even though most people will believe in God at that time, there will still be those who rebel in their hearts.
Isaiah prophesied:
"No longer will there be in it an infant who lives but a few days,
Or an old man who does not live out his days;
For the youth will die at the age of one hundred
And the one who does not reach the age of one hundred
Will be thought accursed." (Isaiah 65:20)
This shows that there will be those who are accursed during the millennial reign who don't reach the age of 100. Such people will be rebels at heart.
"When the thousand years are completed, Satan will be released from his prison, and will come out to deceive the nations which are in the four corners of the earth, Gog and Magog, to gather them together for the war; the number of them is like the sand of the seashore. And they came up on the broad plain of the earth and surrounded the camp of the saints and the beloved city, and fire came down from heaven and devoured them." (Revelation 20:7-9)
So at the end of the thousand years, rebellion will again happen on earth. This rebellion is led by the wicked from among the millennials.
While there is no such term in the Bible as "second fruit" Christians, there will be many believers in God during the thousand year reign. They will rely on Jesus to save them from their sins just as we do.
After the rebellion at the end of the thousand years, God will judge the wicked (Revelation 20:11-15).
After that, God will create a new heaven and new earth.
"He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away." (Revelation 21:4)
"There will no longer be any curse; and the throne of God and of the Lamb will be in it, and His bond-servants will serve Him; they will see His face, and His name will be on their foreheads. And there will no longer be any night; and they will not have need of the light of a lamp nor the light of the sun, because the Lord God will illumine them; and they will reign forever and ever." (Revelation 22:3-5)
So the New Covenant will never pass away. It is by the New Covenant in Jesus' blood that we can live before God forever. And Jesus will be worshipped as King of Kings always.