Perhaps you missed Council of Jerusalem or how Paul is claiming authority over a number of local churches. See Acts.
Missed it not. Paul had long ago been selected for it by the Savior, spent 3 1/2 years in Arabia being taught by Him, then spent 11 years in Tarsus preparong in that Roman/Greek cosmopolitan university town studying Gentile culture, then commissioned by his church at Antioch for the missionary effort. Antioch was not subservient to Jerusalem, neither was any other local church. In unity, yes. In submission to Jerusalem, no. Nor was any of the churches arising from Paul's evangelistic efforts.