Question:Can an elder function as an evangelist and vice versa?
The word "pastor" in Ephesians 4:11 comes from a Greek word referring to a shepherd. This is the man charged with the care and feeding of a flock. As with the office of the evangelist, this office is describe by a variety of words. We can see this in I Peter 5:1-4:
"Therefore, I exhort the elders among you, as your fellow elder and witness of the sufferings of Christ, and a partaker also of the glory that is to be revealed, shepherd the flock of God among you, exercising oversight not under compulsion, but voluntarily, according to the will of God; and not for sordid gain, but with eagerness; nor yet as lording it over those allotted to your charge, but proving to be examples to the flock. And when the Chief Shepherd appears, you will receive the unfading crown of glory."
The word "shepherd" in this passage is a form of the word translated in Ephesians 4:11 as "pastor." Notice the other terms as well. These men are also called elders. This word comes from the Greek word which means an older or senior person. The term indicates that this office is for older men who are experienced with living life as a Christian. The other term is "oversight." Pastors or elders are also called overseers (which is sometimes translated as "bishops"). The word refers to someone who is a superintendent. Here it describes a man who is capable of watching over and directing a congregation. He is a man who is responsible for the congregation.
Another passage that shows these terms being used interchangably is Acts 20:17,28:
"From Miletus he sent to Ephesus and called to him the elders of the church. ... Be on guard for yourselves and for all the flock, among which the Holy Spirit has made you overseers, to shepherd the church of God which He purchased with His own blood."
An elder / pastor / overseer should not be confused with the office of evangelist / preacher / minister. They describe different duties within the church.
At times a man may perform multiple duties, such as Peter being an apostle, a preacher, and an elder (refer again to I Peter 5:1). Provision is made for the support of elders who are also preachers. "Let the elders who rule well be counted worthy of double honor, especially those who labor in the word and doctrine" (I Timothy 5:17). However, do not conclude that every preacher is an elder or that every elder is a preacher. Proof that the jobs can be separate is seen in the apostle Paul who was a preacher, but never was an elder since he did not qualify for the position (he never married) (I Timothy 3:2).