Question: Does God have a distinct role for Gentile and for Jewish believers during the Millennium?
Response: Jewish believers who are not part of the church (i.e., did not believe in Christ until they saw Him in the glory of His Second Coming) will inhabit the complete land of Israel (Gn 15:18-21; 17:7,8; 1 Chr:16:15-18 [15] Be ye mindful always of his covenant; the word which he commanded to a thousand generations;
[16] Even of the covenant which he made with Abraham, and of his oath unto Isaac;
[17] And hath confirmed the same to Jacob for a law, and to Israel for an everlasting covenant,
[18] Saying, Unto thee will I give the land of Canaan, the lot of your inheritance;
See All..., etc.), where Christ will rule over them and the world from the restored throne of David in Jerusalem.
Gentiles who have become believers will live in the rest of the earth as part of what will still be known even in the eternal "new heaven and...new earth" (Rv 21:1) as "the nations of them which are saved" (21:24).