This is a question that is rarely asked in the church today. The assumed answer is almost always "Yes, of course." Whether the term used is elder, overseer, or pastor, most folks in the church believe they should teach.
It is fascinating to look in scripture for examples of elders teaching. What stands out is just how little of it there is. In light of the amount of teaching by elders that goes on in the church today, it seems like it would also be splashed all over the pages of the NT. However, it's just not very frequent at all.
That said, there are passages that I believe indicate that elders should teach. For example, I Timothy 3:2 informs us that overseers should be "able to teach." Although this does not say that they have to teach, it implies strongly that they will be doing so.
In I Peter 5, Peter exhorts the elders to "shepherd the flock of God that is among you." Shepherding can include a fairly wide variety of activities. It seems that teaching would be one of these. Part of shepherding is guidance, and this often takes the form of some type of teaching.
In Acts 20, Paul warns the elders from Ephesus to protect the church against false teachers from both inside and outside the church. One method of doing this is to teach the truth to the people. Paul tells them that some of the false teachers will "speak twisted things." Paul reminds them that he "admonished them with tears." The implication is that the elders must continue to admonish the church by speaking against those who speak twisted things.
Equally important, elders are part of the flock themselves. Paul has commissioned all believers to teach one another. In Colossians 3:16, he writes, "Let the word of Christ dwell in you richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God." As part of the church, elders have this privilege and responsibility.
Whenever we discuss teaching, we must keep in mind that scripture does not limit it to speaking from a podium/pulpit to a relatively silent group of people. Rather, in the bible we see teaching take place in various forms throughout life. It certainly occurred as the church gathered in larger groups, but it also happened when just a few people got together performing normal tasks throughout the day.
Back to the question at hand: Should elders teach? I believe the scriptural answer is a clear "Yes."
In my next post I'm going to tackle a related question that is a little more controversial: Should elders teach in a manner that is different from the way other men in the church teach? Yikes. That should make for an interesting discussion.