I'm only a beginner with Latin, but the first thing that occurred to me as a way to express "the art of leadership" in Latin is:
A quick search turned up a company in England called Ars Ducendi, which teaches leadership. Searching Google Books turned up many hits, including an 1842 commentary on Aristotle's Nicomachean Ethics, written in Latin, which translates στρατηγητικη as ars ducendi et regendi exercitum (the art of leading and governing an army). This book review (I think!) from 1708 mentions describing logic as ars ducendi mentem ad veritatem (the art of leading the mind to truth).
I doubt that ars ducendi was used by the ancient Romans, but it's definitely got some established usage at least in New Latin. While it's not completely soaked with military connotation, it still might not be what you're looking for. If educo fits your meaning as a verb, then perhaps this what you're looking for:
A quick search turns up two occurrences (also New Latin). I don't have as good a feeling for the meaning of ēdūcō. I understand it to literally mean leading something out of something, but easily taking secondary and poetic senses of leading out of something lower or unworthy or merely inactive, into action or something higher. Lewis & Short mention secondary senses of leading troops in march, assisting in childbirth, and raising a child (among others more prosaic). Wiktionary illustrates ēdūcō with this quotation from Exodus:
Ego sum Dominus Deus tuus, qui eduxi te de terra Aegypti, de domo servitutis.
I am the Lord thy God, who hath brought thee out of the land of Egypt, out of the house of bondage.
Jerome's Latin here seems more poetic than the KJV. If the art that you want to name is the art of leading people (metaphorically) out of the house of bondage and into the promised land, ars educendi might work, though it requires giving ēdūcō a restricted sense (which, as Joe Derfner said, is often necessary and customary due to Latin's relatively small vocabulary). Happily, the second e distinguishes it from ars educandi, the art of educating.
Hopefully someone more knowledgeable can comment on the appropriateness of either of these phrases. I don't have enough exposure to Latin writings to be fully confident.