The classical inquiry
Ambition in the Greek tradition is closest to philotimia, "love of honour," with related words (philarchia, love of rule; philodoxia, love of glory) shading the same field. The ancient treatment is characteristically two-eyed: love of honour can be the spur of a serious public life and the discipline of a young person of character; the same impulse, ungoverned, deforms the person who holds it and the polity they belong to.
Aristotle's Nicomachean Ethics discusses philotimia among the virtues and the vices of honour-seeking, treating it as something that can be admired in due measure and as something that, in excess, becomes a recognisable failing. Plutarch is the great classical case study: the Parallel Lives are read, again and again, as a long study of how ambition makes a great public life and how the same ambition, turned in a slightly different direction, undoes one.
What the tradition adds
The Roman moral tradition treats ambitio with marked suspicion — the word itself originally describes the canvassing for office, "going around" for votes. Cicero, Seneca and the historians (Sallust, Tacitus) all return to the difference between honest political ambition and the corrupting kind, often using specific careers as case studies in the same way Plutarch does.
The Christian tradition, especially Augustine in the City of God, reads the libido dominandi — the lust for mastery — as the deforming root of much of the classical Roman story it inherits. Early-modern and Enlightenment thought partially rehabilitates ambition as a publicly productive passion, often by reading the classical texts more sympathetically than the medievals had.
Why it matters for Virtue & Power
Ambition is the question on which the relation between virtue and power turns most sharply. A polity full of people with no public ambition has one set of problems; a polity full of people whose ambition has slipped its moral moorings has another. The classical sources discuss the question with notable care, and the platform reads them in that spirit.