A Presbyterian church is governed by a Session composed of elders who are elected by the congregation. UPC is related to other churches in the denomination through a series of governing bodies.

The Session, which governs the local church, is the first level. Presbytery is the second level governing body and is composed of the ministers and one or more elders from each church within the bounds of the Presbytery. The third level is the Synod, composed of representatives from each Presbytery within its bounds. UPC is part of the Presbytery of South Louisiana and the Synod of the Sun, which encompasses Texas, Oklahoma, Arkansas, and Louisiana.

The highest church governing body is the General Assembly of the Presbyterian Church (USA), with voting commissioners selected from each Presbytery. Elders elected by the congregations may be asked to serve on these higher governing bodies. Authority in the Presbyterian Church resides in the duly elected representatives to the appropriate church governing bodies. Thus, no Presbyterian congregation is a law unto itself.

The Session of University Presbyterian Church consists of the Pastor, and eighteen elders elected by the congregation, usually for three-year terms. The Session is moderated by the Pastor. An elder serves as Clerk of the Session.

The congregation also elects a Board of Deacons composed of sixteen members. The Board of Deacons is under the jurisdiction of the Session. The primary function of the deacons is to minister to those who are in need, to the sick, and to people in distress. The deacons also assist in maintaining the church property and in furthering fellowship in the congregation.