Clement

Clement (~30 AD - ~100 AD) is also known as Saint Clement of Rome or Pope Clement I, although there was certainly no office of Pope in his lifetime.  He was a bishop (i.e. overseer) in the church at Rome, and Roman Catholic tradition says he was appointed by the Apostle Peter himself and is the same Clement that is mentioned in Philippians 4:3.  (I find the latter point doubtful, but no one knows for sure.)  He was banished by the Emperor Trajan to Crimea in the Ukraine to work in a stone quarry and was most likely martyred there.

He is known mainly for his letter to the church in Corinth, known as 1 Clement or the Epistle of Clement.  It was written in the mid-90's AD and is probably the oldest document from the early church that was not included in the New Testament.  In it, he apologizes for being tardy in addressing a dispute in the Corinthian church due to "sudden and repeated calamities and reverses which are befalling us," presumably referring to persecution that occurred under the Emperor Domitian.  He also refers to the deaths of the Apostles Peter and Paul, and mentions that Paul "reached the farthest bounds in the West" (1 Clem 5:6), apparently confirming that Paul completed his planned journey to Spain (Rom. 15:24, 28).

The issue in the Corinthian church was the removal of some elders, and Clement rebukes the people in the church who did this.  Apparently it was not due to any sin on the part of the leaders, but "for the sake of one or two persons." (1 Clem. 47:6)

Clement uses the terms "elders" and "overseers" interchangeably, just as they are used in the New Testament, and he refers to the leaders of the Corinthian church in the plural.  He also mentions "deacons" as serving the overseers/elders.  There is no sense that Clement considered himself to have any authority over the Corinthian church and he gives himself no title in the epistle.  Despite the Roman Catholic church assigning him the title "Bishop of Rome" centuries later, there is no evidence anyone called him that during his lifetime.  He writes as a brother who is on an equal footing with a fellow church.
"These things, dearly beloved, we write, not only as admonishing you, but also as putting ourselves in remembrance. For we are in the same lists, and the same contest awaiteth us."  1 Clem 7:1

There is a passage in this epistle used by the Roman Catholic church to affirm the succession of the popes beginning with Peter.  Clement says:
"And our Apostles knew through our Lord Jesus Christ that there would be strife over the name of the bishop's office.  For this cause therefore, having received complete foreknowledge, they appointed the aforesaid persons, and afterwards they provided a continuance, that if these should fall asleep, other approved men should succeed to their ministration. Those therefore who were appointed by them, or afterward by other men of repute with the consent of the whole Church, and have ministered unblamably to the flock of Christ in lowliness of mind, peacefully and with all modesty, and for long time have borne a good report with all these men we consider to be unjustly thrust out from their ministration."  1 Clem 44:1-2

From the context of the epistle, it is clear that Clement is simply saying that the overseers who were appointed by the original Apostles were expected to be replaced when they died.  It's also interesting to see leaders were appointed "with the consent of the whole Church" and not by a single leader in authority over that church.

From my reading of the epistle, Clement's main arguments why the Corinthian church should not have deposed its overseers are:

1. They were appointed by the Apostles and the church should not overrule the decisions of the Apostles, as they were appointed by Jesus Christ personally.  I already quoted 1 Clem. 44:2 above, and 1 Clem. 42:4 says in regards to the Apostles:
   
   "So preaching everywhere in country and town, they appointed their firstfruits, when they had proved them by the Spirit, to be bishops and deacons unto them that should believe." 
   
   
2. The authority structure in the church is rooted in the Old Testament, and should not be challenged.  Clement quotes Isaiah 60:17 when he says:
   "And this they did in no new fashion; for indeed it had been written concerning bishops and deacons from very ancient times; for thus saith the scripture in a certain place, I will appoint their bishops in righteousness and their deacons in faith."  1 Clem. 42:5
   Note that Isaiah 60:17 (NIV) actually says, "I will make peace your governor and righteousness your ruler."  Clement also refers to God's choice of Aaron as priest (1 Clem 43), implying the absolute and life-long nature of the office. 

The key point that Clement's epistle demonstrates is that immediately after the New Testament is closed, the churches appear to be operating using the model of leadership outlined in the New Testament itself, namely plurality of elders/overseers and each church operating under its own autonomy but in relationship to neighbouring churches and leaders.  However, as Broadbent notes: "Yet even here the beginning of a distinction between clergy and laity is already evident, drawn from Old Testament ordinances." (The Pilgrim Church, p. 31)  The change in perspective is subtle, but these seeds of basing the authority of church leaders on Old Testament models and of the establishment of an hierarchical model of church authority would produce a lot of problems in the years that followed.