Lay ministry is a term used for members of faiths and Christian denominations who are not full-time paid clergy, or not ordained clergy, but who perform the same or similar function.
The United States Conference of Catholic Bishops uses the term Lay ecclesial ministry for a category of non-ordained pastoral ministers.
The Church of Jesus Christ of Latter-day Saints uses the term lay ministry to describe the bishops, stake presidents and other ecclesiastical leaders that are not full-time or paid clergy.
References
Lay ministry Wikipedia(Text) CC BY-SA