There are three possibilities here:
First, this could be a reference to Daniel 12:3, which states: “Those who have insight will shine brightly like the brightness of the expanse of heaven, and those who lead the many to righteousness, like the stars forever and ever.” Under this view, God would be promising believers that they will be rewarded for their faithfulness.
Second, this could be a reference to Revelation 22:16, which states: “I, Jesus, have sent My angel to testify to you these things for the churches. I am the root and the descendant of David, the bright morning star.” Under this view, Christ would be promising himself to these faithful believers.
Third, this could be a reference to Numbers 24:17, which states: “I see him, but not now; I behold him, but not near; a star shall come forth from Jacob, a scepter shall rise from Israel, and shall crush through the forehead of Moab, and tear down all the sons of Sheth.” Under this view, Christ—the morning star of Revelation 22:16—is the fulfillment of this messianic prophecy from Balaam. He is the protector of believers, and he will judge the immoral people that are threatening the church. This makes sense in light of verse 14 (“…you have there some who hold the teaching of Balaam…”).
This author holds to a blending of option two and three. Even though these believers were being tempted to fall in with the Pagan culture around them, Christ promised the faithful that they would reign with him as the messiah promised in the OT.