Hosea which Paul is referencing is speaking about the Kingdom of Israel that was split in two and divorced from God and he then called them "not my People" but later on in Hosea he goes on to say he will forgive them and he will call them "You are my people". These were the Northern Kingdom who were cast among the nations as Gentiles. Not any ordinary Gentiles but people that were once part of Israel.
Prophecies of Jesus fulfilled, as shown by Gentiles believing in God---
so that the Gentiles may glorify God for his mercy, as it is written: “therefore I will praise you among the Gentiles; I will sing hymns to your name.”
Again, it says,
“Rejoice, O Gentiles, with his people.”
And again,
“Praise the Lord, all you Gentiles,
And sing praises to him, all you
Peoples.”
And again, Isaiah says,
“The Root of Jesse will spring up,
one who will arise to rule over the
Nations;
The Gentiles will hope in him.”
Read this Old Testament scripture, it is quoted in the New Testament:
2 Samuel 22:50 Therefore I will praise you, LORD, among the nations; I will sing the praises of your name.
Romans 15:9
and, moreover, that the Gentiles might glorify God for his mercy. As it is written: "Therefore I will praise you among the Gentiles; I will sing the praises of your name."
...And these scriptures:
Romans 15:11
And again, "Praise the Lord, all you Gentiles; let all the peoples extol him."
Psalm 117:1 Praise the LORD, all you nations; extol him, all you peoples.
Psalm 66:4 All the earth bows down to you; they sing praise to you, they sing the praises of your name."