What was Paul's apostleship meant to accomplish?

Paul's apostleship was received to produce obedience to the faith among all nations for Christ's name. It was not directed toward a faith, but the faith—the one faith—and extended to every nation, fulfilling God's purpose through the risen Son.

Les teaches that Paul returns to his apostleship in this text, saying that through the risen Son “we have received grace and apostleship for obedience to the faith.” Les emphasizes that it is “not a faith,” but “the faith”—there is only one—and that this apostleship is “among all nations, for His name.” The surrounding context ties Paul's commission to the resurrection, by which Christ is declared to be the Son of God with power according to the Spirit of holiness. So Paul's apostleship was meant to bring about obedience to the one faith among all nations for His name.

Romans 1:5

By whom we have received grace and apostleship, for obedience to the faith among all nations, for his name:

How is Paul's apostleship connected to the resurrection of Christ?

Paul's apostleship is received through the risen Christ, who was declared the Son of God with power by the resurrection from the dead. Through that same resurrected Christ, Paul received grace and apostleship for obedience to the faith among all nations, not a faith, but the faith.