Does the Bible say anything about them?

The English words "pastor" and "shepherd " both have exactly the same meaning - someone who cares for the sheep. In the New Testament they are both used to translate the same Greek word "poimen." 

The Lord Jesus is the Senior Pastor 

Psalm 23 could be translated, "The Lord is my Pastor." 

Psalm 80, "The Pastor dwells between the Cherubim" 

John:10:11, "The good Pastor gives His life for the sheep." 

1 Peter 5:4, "and when the Senior Pastor (Chief Shepherd) appears, you will receive the crown of glory that does not fade away.

Elders are pastors 

Paul to the elders at Ephesus, Acts 20:28, 

"Therefore take heed to yourselves and to all the flock, among which the Holy Spirit has made you overseers, to pastor the church of God which He purchased with His own blood." 

Peter to the elders of the dispersion, 1 Peter 5:1-2 

"The elders who are among you I exhort, I who am a fellow elder and a witness of the sufferings of Christ, and also a partaker of the glory that will be revealed: Pastor the flock of God which is among you, serving as overseers, not by compulsion but willingly, not for dishonest gain but eagerly nor as being lords over those entrusted to you, but being examples to the flock and when the Senior Pastor appears, you will receive the crown of glory that does not fade away." 

The New Testament church could be described as a group of believer-priests led by a team of pastor-elders.   

The Lord Jesus is both the High Priest and Senior Pastor. 

The New Testament church has multiple pastors - usually called elders. There may also be others in the church doing pastoral work who are not members of the official eldership. The gift of pastoring is one of the spiritual gifts, and this is not confined to the elders. 

The logical consequence of this is that it is wrong to call any one person the pastor of a church, as this implies that  there is only one pastor and that consequently the elders (and others with the gift of pastor) are not pastors. 

As the elders of a church are pastors, any full-time employee or worker associated with a local church should not be called "the pastor."   If a title is needed, an alternative title such as youth worker, youth facilitator, pastoral assistant, administrator or musical director could be considered.