The Bible Says
Elders (plural) were appointed in each church. These men were called elders, bishops (overseer) or pastors.
"Paul and Barnabas appointed elders for them in each church and, with prayer and fasting, committed them to the Lord in whom they had put their trust."
Acts 14:23

"Now the overseer must be above reproach, the husband of but one wife, temperate, hospitable, able to teach, not given to drunkenness, not violent but gentle, not quarrelsome, not a lover of money. He must manage his own family well and see that his children obey him with proper respect. (If anyone does not know how to manage his own family, how can he take care of God's church)?"
I Timothy 3:2-5

"To the elders among you, I appeal as a fellow elder, a witness of Christ's sufferings and one who also will share in the glory to be revealed. Be shepherds of God's flock that is under your care, serving as overseers- not because you must, but because you are willing, as God wants you to be; not greedy for money, but eager to serve, not lording it over those entrusted to you, but being examples to the flock. And when the Chief Shepherd appears, you will receive the crown of glory that will never fade away."
I Peter 5:1-4

Each local church has its own leadership, selected from among the local believers.