Revelation 22:14

that they may have the right to the tree of life
They may have the right to the tree of life is ἔσται ἡ ἐξουσία αὐτῶν ἐπὶ [estai hē exousia autōn epi] : it will be the authority of them over the tree of life. The right to the tree of life is universal to all believers. No mention is made of two categories of the redeemed in eternity: those who require access to the tree and those who do not. Neither is there mention of some who eat the fruit and others who only use the leaves. See commentary on Revelation 22:2.

may enter through the gates into the city.
Those who are born-again are the overcomers. Through the power of the Holy Spirit they will also be those who do the commands of the Lord. They are among the redeemed who are written in the Book of Life and therefore avoid the second death which is being cast into the Lake of Fire (Rev. Rev. 21:15+). They have full access to the New Jerusalem whose gates are never closed (Rev. Rev. 21:24-26+). All the redeemed have access through the gates. Access through the gates is equivalent with rights to the tree of life because the tree is within the city. To access the tree, one must first go through the gates. See commentary on Revelation 21:24.

Notes

¹ “The [TR] reading appears to be a scribal emendation, for elsewhere the author uses the expression τηρεῖν τὰς ἐντολάς [tērein tas entolas] (Rev. Rev. 12:17+; Rev. 14:12+).”—Bruce M. Metzger, A Textual Commentary on the Greek New Testament (Stuttgart, Germany: Deutsche Bibelgesellschaft, 1994), Rev. 22:14.