A popular turn of phrase among MAD is to pay attention
who is being spoken to.
With that in mind, consider how this starts out in verse 4, and then when reading the following verses use a concordance to check out the cross reference verses it gives for each of the verses.
Romans 15:4-12 ESV
(4) For whatever was written in former days was written for our instruction, that through endurance and through the encouragement of the Scriptures we might have hope.
(5) May the God of endurance and encouragement grant you to live in such harmony with one another, in accord with Christ Jesus,
(6) that together you may with one voice glorify the God and Father of our Lord Jesus Christ.
(7) Therefore welcome one another as Christ has welcomed you, for the glory of God.
(8) For I tell you that Christ became a servant to the circumcised to show God's truthfulness, in order to confirm the promises given to the patriarchs,
(9) and in order that the Gentiles might glorify God for his mercy. As it is written, “Therefore I will praise you among the Gentiles, and sing to your name.”
(10) And again it is said, “Rejoice, O Gentiles, with his people.”
(11) And again, “Praise the Lord, all you Gentiles, and let all the peoples extol him.”
(12) And again Isaiah says, “The root of Jesse will come, even he who arises to rule the Gentiles; in him will the Gentiles hope.”
Paul is fulfilling what God wanted all along for Israel to be ---- a light unto the whole world to seek Him and be their God.
Paul, an Israelite himself, was a remnant believer of Israel.
Romans 11:1-5 ESV
(1) I ask, then, has God rejected his people? By no means! For I myself am an Israelite, a descendant of Abraham, a member of the tribe of Benjamin.
(2) God has not rejected his people whom he foreknew. Do you not know what the Scripture says of Elijah, how he appeals to God against Israel?
(3) “Lord, they have killed your prophets, they have demolished your altars, and I alone am left, and they seek my life.”
(4) But what is God's reply to him? “I have kept for myself seven thousand men who have not bowed the knee to Baal.”
(5) So too at the present time there is a remnant, chosen by grace.