It is only reasonable that the Lord Jesus should be the One who oversees the church that belongs to Him. In 1 Peter 5:4 we are told that He is the Chief Shepherd of the flock of God. We are also given specific direction regarding the fact that Christ has ordained there to be human shepherds under His authority to carry out the responsibility of exercising oversight of the flock until He Himself comes (1 Peter 5:1-4Therefore, I exhort the elders among you, as your fellow elder and witness of the sufferings of Christ, and a partaker also of the glory that is to be revealed, shepherd the flock of God among you, exercising oversight not under compulsion, but voluntarily, according to the will of God; and not for sordid gain, but with eagerness; nor yet as lording it over those allotted to your charge, but proving to be examples to the flock. And when the Chief Shepherd appears, you will receive the unfading crown of glory.). The apostle Paul spoke of the fact that it is the Holy Spirit who makes known those who are to be elders in the church (Acts 20:28Be on guard for yourselves and for all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood.). It seems obvious that God's people will recognize who these men are as they carefully consider the qualifications set forth in God's word, and as they are responsive to the ministry of God's Spirit among them.
