When we use the term evangelist, we think of someone such as George Whitefield or Billy Graham, a person who travels to different places preaching to non-Christians. But that is not how the term was understood by previous generations. For example, the Form of Presbyterial Government, a document adopted by the Church of Scotland when it adopted the Westminster Confession of Faith, says: ‘The officers which Christ hath appointed for the edification of his church, and the perfecting of the saints, are, some extraordinary, as apostles, evangelists, and prophets, which are ceased. Others ordinary and perpetual, as pastors, teachers, and other church-governors, and deacons.’
The older view was that ‘evangelists were ordained persons (2 Tim. 1:6), whom the apostles took as their companions in travel (Gal. 2:1), and sent them out to settle and establish such churches as the apostles themselves had planted (Acts 19:22), and, not being fixed to any particular place, they were to continue till recalled, 2 Tim. 4:9’ (Matthew Henry).
Only two people are described as evangelists in the New Testament: Philip (Acts 21:8 8: ‘On the next day we departed and came to Caesarea, and we entered the house of Philip the evangelist, who was one of the seven, and stayed with him’) and Timothy (2 Timothy 4:5: ‘As for you, always be sober-minded, endure suffering, do the work of an evangelist, fulfil your ministry).
Albert Barnes, the nineteenth-century commentator, wrote of evangelists: ‘What was the precise office of the evangelist in the primitive church, it is now impossible to determine. The evangelist may have been one whose main business was preaching, and who was not particularly engaged in the government of the church. The word properly means “a messenger of good tidings”; and Robinson supposes that it denotes a minister of the gospel who was not located in any place, but who travelled as a missionary to preach the gospel, and to found churches. The word is so used now by many Christians, but it cannot be proved that it is so used in the New Testament.’
A recent supporter of the interpretation that the office of an evangelist was found only at the beginning of the church was Martyn Lloyd-Jones. He says: ‘Sometimes he was sent ahead of the apostles, as Philip was sent to Samaria, but generally he followed the apostles…. He thus supplemented the work of the apostles and extended it and caused it to spread and to become established. Thus the evangelist was a man whose office was temporary, and as the churches were established and became more settled, that office likewise disappeared.’
As you can perhaps deduce, I don't know what an evangelist was in Paul's time. And it looks as if not many others do either. Whoever they were, they were important because they were gifts of Jesus to his church. If evangelists in this sense of the word were temporary gifts, then here we have a reminder of the sovereignty of Jesus who decides when certain gifts are needed for the benefit of his people. So while he may no longer give this particular gift, we can deduce that he will give the exact gifts that we need.