Was what Paul says here given by the inspiration of the Holy Spirit?
Yes, the passage affirms that what Paul says was given by the inspiration of the Holy Spirit. The context states that as the Holy Spirit inspired him, he spoke about not giving place by subjection to the Jerusalem leaders, so the truth of the gospel might continue with the Gentiles.
Les explains that Paul's words were by inspiration, and he says he will never take that away from him—that as the Holy Spirit inspired him, he addressed these men in Jerusalem: Peter, James, John, and the rest. Les notes Paul was under pressure, but he says they did not give in to them, no, not for an hour, so that the truth of the gospel might continue with the Gentiles.
To whom we gave place by subjection, no, not for an hour; that the truth of the gospel might continue with you.