Summary: What is congregational responsibility to elders? How does a congregation honour the elders?
“Let the elders who rule well be considered worthy of double honor, especially those who labor in preaching and teaching. For the Scripture says, ‘You shall not muzzle an ox when it treads out the grain,’ and, ‘The laborer deserves his wages.’ Do not admit a charge against an elder except on the evidence of two or three witnesses. As for those who persist in sin, rebuke them in the presence of all, so that the rest may stand in fear.” 
It is not self-serving for me to teach Christian responsibility to honour elders who labour among us, preaching and teaching. There must be an unwritten rule that preachers are not supposed to speak about money; especially are they to be silent concerning support for their service to the people of God offered before the Lord. Nevertheless, the Word of God addresses this matter forthrightly; and if we will honour God we will understand what has been delivered by God.
At the outset, I need to say that I am not paid what I am worth—fortunately. I confess, I am an unworthy servant of Christ the Lord; I have only done what was my duty [cf. LUKE 17:10]. However, with the Apostle, I magnify my ministry [cf. ROMANS 11:13], received by appointment from the Risen Son of God. I am conscious that God Himself has appointed me to serve as an elder; and since receiving His appointment, I have endeavoured with all the energy of Christ that works powerfully within me to fulfil this service to the praise of His glory [see COLOSSIANS 1:29].
I did not enter the service of Christ for what I might earn—I had a superior income potential when I pursued scientific endeavours. I entered Christ’s service because of the pressing weight of glory that accompanied the call of God—I was compelled to preach the message of Christ the Lord. I understand only too well and from experience the Apostle’s statement concerning the proclamation of the Word. Paul wrote, “If I preach the gospel, that gives me no ground for boasting. For necessity is laid upon me. Woe to me if I do not preach the gospel! For if I do this of my own will, I have a reward, but if not of my own will, I am still entrusted with a stewardship. What then is my reward? That in my preaching I may present the gospel free of charge, so as not to make full use of my right in the gospel” [1 CORINTHIANS 9:16-18].
I was miserable when I wasn’t digging into the Word; I was disconsolate when I was not proclaiming the message of Christ the Lord. The situation has not changed in the ensuing years. I have not sought wealth in my service before the Lord; I have laboured to speak the truth in love to a generation that is woefully ignorant of love. I have not sought to flatter anyone; I have struggled to present the message of Christ without prejudice. I can say with confidence that I have lived off the gifts of God’s people, generously supplied by the congregations I have served. Through His people, Christ has provided all that was necessary to ensure that I was not reduced to penury.
Therefore, whatever I may say concerning honouring those who serve you, you may be assured that I do not seek anything for myself. Again, as the Apostle has stated so eloquently, I am not “speaking of being in need, for I have learned in whatever situation I am to be content. I know how to be brought low, and I know how to abound. In any and every circumstance, I have learned the secret of facing plenty and hunger, abundance and need. I can do all things through him who strengthens me” [PHILIPPIANS 4:11-13]. I do seek Christ’s glory, just as “I seek the fruit that increases to your credit” [PHILIPPIANS 4:17].
THOSE HONOURED — “Let the elders who rule well be considered worthy of double honor, especially those who labor in preaching and teaching” [1 TIMOTHY 5:17]. In many respects, the churches of this day resemble the church in Ephesus; this is obvious from several notable views. In each church, there will be found elders who are worthy of commendation. By the same token, too frequently there are found elders deserving censure. Paul sets the standard for both commendation and censure in the text we are considering.
Because Paul takes up this theme at this point in the missive, the implication could be drawn that there was a foundational flaw in the structure of the eldership in this congregation. Perhaps some of the false teachers had managed to insinuate themselves into the eldership; or perhaps some of them had actually come from within the eldership. Paul had warned this particular eldership that such a thing was not only a possibility, but it was a likely scenario. “I know that after my departure fierce wolves will come in among you, not sparing the flock; and from among your own selves will arise men speaking twisted things, to draw away the disciples after them” [ACTS 20:29, 30].