There shall be no night there
The NU text and some manuscripts in the line of the MT text omit there implying the general absence of darkness, whether in the city or elsewhere. See commentary on Revelation 21:23.
They need no lamp nor light of the sun, for the Lord God gives them light
Gives them light is φωτίσει ἐπʼ αὐτούς [phōtisei ep autous] , present tense: He is shining upon them. Those within the vicinity of the New Jerusalem will receive the radiant light of Gods glory. This is the message which we have heard from Him and declare to you, that God is light and in Him is no darkness at all (1Jn. 1Jn. 1:5). They will have no need of the sun, although the sun may still be present in the eternal state. See commentary on Revelation 21:23.
they shall reign forever and ever
Their initial reign is for one thousand years during the Millennial Kingdom (Rev. Rev. 20:4-6+). See Millennial Reign of the Saints. After the throne of the Son is merged with the Father, the saints continue to co-reign with Him in eternity. In Daniels night vision, the angel explained, the saints of the Most High shall receive the kingdom, and possess the kingdom forever, even forever and ever (Dan. Dan. 7:18).
Jesus told the church at Thyatira that the overcomer would co-rule with Him (Rev. Rev. 2:27+). See commentary on Revelation 2:27. He also told the church at Laodicea that the overcomer would sit with Him on His throne (Rev. Rev. 3:21+). See commentary on Revelation 3:21.