Aristotle doesn't end Ethics so much as begin Politics. He's an overachiever like that.
He moves from a discussion about how awesome the contemplative life is into a rant about the education of those who practice the political art. It might be hard to see the connection between a discussion about human happiness and the need for a better system of education for the next generation of lawmakers.
But not if you're viewing the world from the inside of Aristotle's brainpan: Ethics and Politics are considered a continuous series of lectures on the experience of humans in community. The movement into governance as an important part of the common good seems like the natural next step.
After all—and check out our Symbols section for more on this—the city and the individual aren't so very different, according to Mr. A. One has more houses and infrastructure, but they're ruled in pretty similar ways.