In confessional Reformed and Presbyterian circles, elders are typically elected by the congregation based on the qualifications in 1 Timothy 3 and Titus 1. Although it differs a bit in various Reformed and Presbyterian churches, typically men who are elected to the office of elder serve for several years (i.e. 3), then take several years “off,” then sometimes serve again (assuming the elder doesn’t move away, get divested of his office, or become unable to serve for serious health/personal reasons.).
But is this type of “term” or “class” eldership the most biblically prudent way to go? John Murray says it is not. He argues that the office of elder is a lifetime office. I tend to agree. Here are some points Murray makes against term eldership:
“…The idea of being ordained to office for a limited period of time is without warrant from the New Testament, and is contrary to the implications of election and ordination. …While the New Testament does not expressly legislate against term eldership, there are considerations which fall into the category of good and necessary inference, and which militate against the propriety of this practice. These considerations are derived from the implications which underlie or inhere in the acts of electing and ordaining to this office, implications which are incompatible with the idea of term eldership.”
“…[First,] the gifts for eldership [i.e. in 1 Tim. 3, Titus 5, Acts 20] are not of a temporary character. …The simple fact is that when a man possesses certain endowments which qualify him for eldership, we must proceed on the assumption that they are abiding, and permanently qualify him for the discharge of the functions of the office.”
“…There is [also] the argument that pertains to the unity of ruling office. In respect of ruling the church of God, the ruling elder and the teaching elder [pastor] are on complete parity. When the teaching elder is ordained, he is ordained to rule as well as to teach, and his ruling function is just as permanent as his teaching function.”
Murray also gives some practical considerations against term eldership: “1) It tends to create in the minds of the people the notion of trial periods. That should have no place whatsoever in the election of elders. 2) It tends to develop such a notion in the minds of elders themselves, and therefore a decreased sense of responsibility and office. 3) It interferes with the continuity, and therefore with the sense of responsibility, as also with the stability of the office. 4) It may occasion the removal of good elders as well as bad ones. 5) It may minister to party division and strife. 6) It is rather liable to give the impression of representative government and of democracy. Presbyterianism is not democratic. 7) It tends to promote the idea that the eldership should be passed around.”
Of course Murray gives more biblical and practical defense of his position. You can read the entire article in Volume 2 of his Collected Writings and it is also found (with some helpful explanation) in Witmer’s The Shepherd Leader.