The book of Revelation is a series of mini-visions each beginning with a phrase such as, "I saw." This mini-vision in question is then:
Rev 21:2-8 NHEB 2 I saw the holy city, New Jerusalem, coming down out of heaven from God, made ready like a bride adorned for her husband. 3 I heard a loud voice from the throne saying, “Look, the tabernacle of God is with humans, and he will dwell with them, and they will be his people, and God himself will be with them and be their God. 4 And he will wipe away every tear from their eyes, and death will be no more, nor will there be mourning, nor crying, nor pain, anymore, for the first things have passed away.” 5 He who sits on the throne said, “Look, I am making all things new.” He said, “Write, for these words are faithful and true.” 6 He said to me, “It is done. I am the Alpha and the Omega, the Beginning and the End. I will give freely to him who is thirsty from the spring of the water of life. 7 He who overcomes, I will give him these things. I will be his God, and he will be my son. 8 But for the cowardly, unbelieving, abominable, murderers, sexually immoral, sorcerers, idolaters, and all liars, their part is in the lake that burns with fire and sulfur, which is the second death.”
So, we have described for us the outcome of two classes of people, (verse 7) those who overcome and (verse 8) the cowardly, unbelieving, et al.
The promise you ask about is for the first class of people, "those who overcome," verse 7.
A mini-vision or three previously, John described the same two classes of people and their respective outcomes: the blessed and holy witnesses for Christ (verses 4b & 6) contrasted against the rest of the dead (verse 5).
Rev 20:4b-6-10 NHEB 4b I saw the souls of those who had been beheaded for the testimony of Jesus, and for the word of God, and such as did not worship the beast nor his image, and did not receive the mark on their forehead and on their hand. They lived, and reigned with Christ for a thousand years. 5 (The rest of the dead did not live until the thousand years were finished). This is the first resurrection. 6 Blessed and holy is he who has part in the first resurrection. Over these, the second death has no power, but they will be priests of God and of Christ, and will reign with him one thousand years. 7... 8... 9... 10... .
11 I saw... [next mini-vision].