The only example I could think of is St. Clement’s letter to the Corinthians. The Church of Corinth had rid itself of it’s bishop and most of its priest and replaced them with priest chosen by the flock. This went against the Apostolic appointments, probably of St. Paul.
Anyway, Pope Clement, in the 80’s or 90’s, wrote a letter to the Church admonishing them, and exhorting them to restore the original bishop and priests to the previous roles. From his letter, it is safe to assume that Pope Clement is responding to a request from the Church of Corinth to help resolve this issue, even though the Apostle John was still alive, and ignoring the secular animosity between the city of Corinth and the empire of Rome.
The Church in Corinth received the letter (and chastisement) from Clement with great fanfare. The letter was read during the Liturgy Service for decades after the incident. The Early Church seriously considered the letter to be inspired Scripture, but it did not make it into the Canon.
The letter itself, if I’m correct, followed along the same vein as St. Paul’s numerous Epistles. There is a problem in a local church. The matter is brought up to St. Paul. His Epistle is meant to deal with this matter.