Non duality - does it quash ambition? If you have fully  '" arrived" at non duality is there a threat that you won't have ambition? Isn't ambition a driving force in human life ?
Good question. There are several schools of thought here. 

According to one, attainment of nonduality does leave the person with nothing else to be done. No goals, no ambitions.

What follows from this is an idea that before a student is introduced to nonduality, they must be first taught discipline and a high-drive attitude, so by the time they attain non-duality, they develop a habit of being strong. A kind of prophylactics against the nondual depression, we could say. 

According to another school, even though there is a clear realization that in nonduality no goals make absolute sense, relatively speaking some things are still locally "better" than others, so some local goals may still make relative sense. In this context, if someone has eyes to see local problems, they will remain motivated even if globally nothing makes sense. 

Finally, according to my teacher, having goals post-enlightenment is more like playing Make-Believe. One doesn't actually buy into these things, so it's not like a true (blind) ambition. But an enlightened being may act as if they were seriously engaged with something, more for the sake of others, and even for an enlightened kind of "fun", than out of greed to achieve anything.  

In (Mahayana) Buddhism, they define Enlightenment as "union of wisdom and compassion" for this very reason. Wisdom refers to realization of emptiness or nonduality, which sees that both suffering and so-called sentient beings are empty. Compassion is seeing that, however empty, the experience of suffering is rather painful -- hence the drive (=ambition?) to help out.