A "young pastor" refers to a person who is relatively new in their career as a religious leader or minister and is generally young in age. Full definition
His thoughts and especially his attitudes have accompanied me ever since in my training of young pastors and my work in the leadership of the church. (religion-online.org)
But when a new young pastor was hired, he wanted a cooler band to get more young people, and the first thing to go were the older women. (sarahbessey.com)