Summary: God's design appears to be a plurality of elders to oversee the labours of a congregation.
“This is why I left you in Crete, so that you might put what remained into order, and appoint elders in every town as I directed you—if anyone is above reproach, the husband of one wife, and his children are believers and not open to the charge of debauchery or insubordination. For an overseer, as God’s steward, must be above reproach. He must not be arrogant or quick-tempered or a drunkard or violent or greedy for gain, but hospitable, a lover of good, self-controlled, upright, holy, and disciplined. He must hold firm to the trustworthy word as taught, so that he may be able to give instruction in sound doctrine and also to rebuke those who contradict it.” 
Following establishment of a church, the appointment of elders must surely qualify as one of the most vital tasks facing the church planter. Clearly, this task was a priority for the Apostle Paul since we are told that he, in concert with Barnabas, appointed elders in each church [e.g. ACTS 14:23]. Writing in the text before us, the Apostle specifically directed Titus to complete this vital work of appointing elders to serve the various churches established in Crete. Many of the professed saints of God appear confused about the definition of a church; therefore, it should not be surprising that believers appear cavalier about the appointment of elders.
What is a New Testament church? What qualifies a congregation to be identified as a New Testament church? In simple terms, a New Testament church is a congregation that reflects the characteristics of churches described in the New Testament. By that criterion, we must note that many of those churches were obviously dysfunctional and severely flawed; and so are we. We do not wish to cast the churches of that era in mythical proportions; the assemblies were composed of sinners just as the churches of this day are populated with sinners.
A fuller explanation would identify a New Testament church as an assembly of individuals who have believed the Good News that Jesus is the Son of God. Believing that He is God, they are convinced that He was crucified because of their sin and that He was raised from the dead. Openly confessing faith in Jesus as Christ, the twice-born individuals will have been baptised—immersed in water, picturing their confidence in His death, burial and resurrection. United to the Risen Saviour through faith, these redeemed and obedient believers regularly and voluntarily meet to worship Him as the Son of God. Through their mutual worship, they build one another in this holy Faith, advance the cause of Christ through winning others to the Faith and incorporating them into the fellowship of the assembly. Gathered in assembly, the believers practise a congregational polity which calls each individual to submit to the teaching of the Word of God, seeking the Master’s appointment of those whom He wills to lead them in the Word. Those appointed to leadership within a congregation bear the title either of deacons or of elders.