The reign takes place in Heaven. Most people have a misunderstanding of the word "reign" in that context, but scripture defines that "reign" for us.
Look at the passages in Revelation, which speak of "reign", and notice the location, of each:
The “reign upon the earth” comes after 1,000 years [Revelation 20:2,3,4,5,6,7], for the “saints” must be both resurrected and/or translated, glorified, and brought back to Heaven [John 14:1-4; 1 Thessalonians 4:17, etc] at the Second Advent and First Great Resurrection, to “reign” in Heaven, for 1,000 years [Revelation 20:4,5a,6] going over the record books of the lost [1 Corinthians 6:2,3; Psalms 149:1-9]:
[1] The “thousand years” reign “in Heaven” [Psalms 50:5; Matthew 5:3,8,10,12, 6:20, 13:30, 24:31; Mark 10:21, 13:27; Luke 6:23, 18:22, 23:43; John 14:2-3, 17:24; Colossians 1:5; Hebrews 10:34; 1 Peter 1:4; Revelation 7:9, 14:3, 19:1; “Paradise”, Luke 23:43; 2 Corinthians 12:4; Revelation 2:7] with Christ Jesus [1 Thessalonians 4:16-17; Revelation 20:6] and
[2] The “reign on earth” [“made new”, not this sin polluted Earth; 2 Peter 3:13; Isaiah 65:17, 66:22; Revelation 21:1] that lasts “forever and ever” [Revelation 5:10; “meek inherit earth” [“made new”, not this sin polluted Earth], Psalms 37:9,11,34; Proverbs 11:31; Isaiah 25:8, 65:21; Daniel 7:27; Matthew 5:5; Revelation 5:10].
Did you notice the two "reigns"?
[1] limited in time, 1,000 years
[2] infinite in time, 'for ever and ever'
It's kinda like an ascension year, and the full reign afterward.
For instance, look at these texts, and ask yourself, do they say anywhere, in their text or its contexts, that the "reign" spoken of in it, it takes place on earth:
Rev 20:4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ a thousand years.
Rev_20:6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.
Remember, John 14:1-4; 1 Thessalonians 4:17, etc, speak of Jesus second advent:
Joh 14:1 Let not your heart be troubled: ye believe in God, believe also in me.
Joh 14:2 In my Father's house are many mansions: if it were not so, I would have told you. I go to prepare a place for you.
Joh 14:3 And if I go and prepare a place for you, I will come again, and receive you unto myself; that where I am, there ye may be also.
Joh 14:4 And whither I go ye know, and the way ye know.
1Th_4:17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
The saints, translated and resurrected, go "up" and return with Jesus back unto the Father in Heaven, for the duration of the 1,000 years, while the earth remains broken down by the seven last plagues, greatest earthquake, sun and moon being moved out of their places, and the atmosphere being torn asunder, and all the cities broken down and mountains uprooted, seas turned to blood, etc.
It is not until after the 1,000 years that all the saints with Jesus and New Jerusalem return to earth and come down:
Rev 21:2 And I John saw the holy city, new Jerusalem, coming down from God out of heaven, prepared as a bride adorned for her husband.
Zec 14:4 And his feet shall stand in that day upon the mount of Olives, which is before Jerusalem on the east, and the mount of Olives shall cleave in the midst thereof toward the east and toward the west, and there shall be a very great valley; and half of the mountain shall remove toward the north, and half of it toward the south.
Rev 20:9 And they went up on the breadth of the earth, and compassed the camp of the saints about, and the beloved city: and fire came down from God out of heaven, and devoured them.
Zec 14:12 And this shall be the plague wherewith the LORD will smite all the people that have fought against Jerusalem; Their flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth.
Two Jerusalem's will face each other.
Old Jerusalem to the west of the Mount of Olives, and
New Jerusalem, which will have come down with Jesus and the saints, to the East of
Old Jerusalem.
There is no text in scripture which states that the saints "reign" upon the earth for 1,000 years, and every text which shows that they cannot.