Baptism is an ordinance (sacrament, if you will) of the Church (Mat. 28:19, 20). It is to be administrated by those who are "qualified and thereunto called, according to the commission of Christ". Typically this would be either the pastor or elders.
Was Philip in Acts 8:36-40 a Pastor or a Priest ?
Clergy system is never supported by the Bible, I am sure.