What is apostolic succession and where is it in the Bible?

Apostolic succession is the unbroken line of authority running from Christ to the apostles to the bishops they appointed and on to the bishops of today, and it is in the Bible in germinal form in Acts 1:20-26, Acts 14:23, Titus 1:5, and 2 Timothy 2:2, long before the Fathers ever had to defend it. The Catholic claim is simple to state. The Church's authority is a line, and the line leads straight back through the bishops to the apostles and finally to Jesus Christ. The Father sends the Son, the Son sends the Twelve, the Twelve appoint successors, and the successors appoint theirs. Apostolic succession is plainly in evidence in Scripture, which is more than can be said for the doctrine of Bible-only revelation. Begin where the apostles themselves began. In Acts 1:20-26, before Pentecost, before a single word of the New Testament is written, Peter stands up and applies Psalm 108:8 to Judas: "his bishopric let another take." Then the eleven do exactly that, and Matthias is numbered with them. Consider what that establishes. The apostolic office is an office, not a personal charism that dies with the man. It can be vacated and it must be filled. That is succession, and it happens on the very first page of the Church's history. From there the pattern repeats wherever the apostles go. Acts 14:23: Paul and Barnabas appointed elders for them in each church and, with prayer and fasting, committed them to the Lord. Titus 1:5: "For this cause I left you in Crete, that you should set in order the things that are wanting and should ordain priests in every city, as I also appointed you." The Greek is katasteses kata polin presbyterous, literally city by city, and Crete had about half a dozen major cities. Look at the chain of command sitting inside that one verse. Paul could not command Titus to ordain unless Paul had authority over Titus, and Titus could not ordain unless he had authority over the men he ordained. Two verses later Paul slides from presbyteros to episkopos without changing subject, which tells you the two words were still interchangeable in those early years. Peter does the same thing from the other direction when he addresses the elders of the churches as "fellow elders" sharing his authority (1 Peter 5:1). These men are not figureheads. They govern. When the circumcision controversy erupts, it is not only the apostles but the elders who convene at Jerusalem (Acts 15:6), and the complaint against the agitators is not that they lacked a Scripture proof but that "they went out from us without our authorization" (Acts 15:24). Apostles and elders together promulgate the decision and bind the Church to it. The clearest text of all is 2 Timothy 2:2, where Paul tells Timothy to entrust what he heard from Paul in the presence of many witnesses to faithful men who will be able to teach others also. Count the generations in that one sentence: Paul, Timothy, faithful men, others also. Four links. Paul is not describing a temporary arrangement for the apostolic age; he is describing a mechanism designed to run indefinitely. And what is being handed on is not only the written text. Timothy is repeatedly told to guard "the good deposit" and to hold fast to "what you heard from me" and "the things you have heard me say in the presence of many witnesses" (2 Timothy 1:13-14, 6:20). Paul says plainly that his teaching came both by word of mouth and by letter. I want to press one point that is usually skipped. At the end of the apostolic age a buzzer did not sound and a voice did not ring out from heaven announcing that Scripture had just become formally sufficient and that the Church could now dispense with the living authority Christ established. Nothing of the kind happened. The bishops went on doing exactly what the apostles had taught them to do. The one development the New Testament does imply, and Tradition confirms it, is that bishops have no power to promulgate new revelation. Public revelation closed with the death of the last apostle. All a bishop may do is guard what was already given. The earliest Christians outside the New Testament describe the same thing. Around the year 96 Pope Clement of Rome writes to the Corinthians that Christ was sent from God and the apostles from Christ, that the apostles preached from district to district and appointed their first converts as bishops and deacons, and that because they foresaw there would be strife over the office of bishop they added the provision that when these men fell asleep other approved men should succeed them in their ministry. That is a definition of apostolic succession written down within living memory of the apostles. Saint Irenaeus then gives the list. The apostles entrusted the office of the episcopate at Rome to Linus, then Anacletus, then Clement, then Evaristus, Alexander, Sixtus, Telesphorus, Hyginus, Pius, Anicetus, Soter, and Eleutherius, "twelfth from the apostles," who held the see in his own day. Eusebius reports the same beginning and identifies Linus with the Linus Paul greets in 2 Timothy 4:21. Hegesippus, travelling to Rome around 180, says he conversed with a great many bishops and received the same doctrine from all of them. And when the Donatists broke away, Saint Optatus did not argue from a proof text. He recited the entire Roman succession from Peter to Siricius, his own contemporary, and then said: give us the origin of your chair. That is still the question. Anyone who sets up another chair against the one chair is, in Optatus's words, a schismatic and a sinner.