What the Bible says about the pope

If we come to believe that the Bible asserts a leader of the Church (Peter), then it seems clear it follows in logic and common sense that this leader would have successors; that the office would exist in perpetuity. When Judas defected and killed himself, the disciples chose a successor, Matthias, and the Bible uses the word episkopos (“bishop”) to describe the office involved (a key argument for apostolic succession). So why wouldn’t Peter, similarly, also have a successor?