Every time you go this route I simply hear you say, "well, I don't have a good response to what he is saying, so I will blow smoke in his face."
No, when someone says something that everyone except that person knows is complete nonsense, then I call it out as such. I don't believe there is another person in the world who would agree with you that Paul changed the subject from Romans 9:24 to verse 25. So, you need me to spell this out for you? Okay then.
Romans 9:19 One of you will say to me: “Then why does God still blame us? For who is able to resist his will?” 20 But who are you, a human being, to talk back to God? “Shall what is formed say to the one who formed it, ‘Why did you make me like this?’" 21 Does not the potter have the right to make out of the same lump of clay some pottery for special purposes and some for common use? 22 What if God, although choosing to show his wrath and make his power known, bore with great patience the objects of his wrath—prepared for destruction? 23 What if he did this to make the riches of his glory known to the objects of his mercy, whom he prepared in advance for glory— 24 even us, whom he also called, not only from the Jews but also from the Gentiles?
Okay, so throughout this passage Paul is talking about how it is up to God to determine who are His people and who are not, not man. And it's up to God what He wants each person to do and who He will take out His wrath on and so on. And then he points out that God calls not only Jews, but also Gentiles to be His people.
And then he said this:
25 As he says in Hosea: “I will call them ‘my people’ who are not my people; and I will call her ‘my loved one’ who is not my loved one,” 26 and, “In the very place where it was said to them, ‘You are not my people,’ there they will be called ‘children of the living God.’”
This clearly fits the context of what Paul had previously been writing about. He had already been indicating that it is God who determines who His people are, not anyone else. Before verse 25 Paul was indicating that God determines who are His people and who He will take out His wrath on. And then Paul indicated in verse 25 that he will call them "my people" who are not my people. And he points out how He would do that even where "it was said to them 'You are not my people'. This fits the context of what he had just been writing about because it again shows that God is the one who declares who His people are, not anyone else. Many Jews objected to the concept of Gentiles being God's people, but they are. No one can tell God that He can't have Gentiles as His people. As Paul had just said in verse 24, God called not only Jews, but also Gentiles to be His people.
So, this is why I say that there is no basis for claiming that Paul changes the subject in verse 25. He was clearly continuing the subject he had been writing about before that and expanding on it in verses 25 and 26.
Clarifying the OT is not changing it.
Of course not. That's my point. But, you're missing how Paul clarified the meaning of the prophecy of Hosea 2 by indicating that it applies to Gentiles as well.
