hēgeomai

In the New Testament this sense always shows up as a participle used like a noun, "the one who leads" or "those who lead." It never appears as a plain finite verb here. That small fact carries weight: the word describes people by what they keep on doing, not by a fixed office they hold. A leader, in this usage, is one who in ongoing practice goes ahead of the group.

The word covers a wide social range. In the wider Greek world it named village headmen, heads of trade guilds, chairmen of local associations, and even Roman provincial governors. The Greek Old Testament had already made it the standard word for the leader God appoints over his people (נגיד), the figure promised in texts about David. So when the New Testament calls church leaders by this term, the language would have sounded both ordinary to Greek ears and rich with biblical echoes of the shepherd-ruler.

The New Testament writers seem to prefer this flexible word over the more technical titles for church office. In Hebrews the leaders are simply those who "spoke the word of God" to the people and who "keep watch over your souls." Jesus redefines the whole idea in Luke: the one who leads is to be like the one who serves.

This is the far more common use of the word in the New Testament. It names a settled act of the mind, the moment a person sizes something up and assigns it a value. It is stronger than a passing opinion or a customary assumption; it is closer to a verdict reached by weighing the evidence. Greek writers from Plato onward used it for the considered judgments of those who think carefully, and the New Testament writers exploit that weight.

The word often carries the flavor of bookkeeping, of counting one thing as gain and another as loss. Paul puts everything he once prized in the loss column and counts knowing Christ as the only true gain. Moses, in Hebrews, weighs the wealth of Egypt against the reproach of Christ and judges the reproach worth more. The same verb runs through Philippians, James, and the letters of Peter wherever a writer wants a reader to re-rank what matters.

Because the word names a deliberate judgment, the New Testament uses it to ground how people act. The way you appraise reality decides how you live in it. Believers are told to count one another as more important than themselves, to count trials as occasions for joy, and to count God's patience as the opening of salvation, while the writers expose false teachers who count wrongdoing as pleasure and scoffers who count God's delay as failure.