Viewed in one way, ambition is a good thing, and its absence in people, especially in the young, we consider to be a defect. Without ambition, there can be no realization of one's potential. Happiness is connected with the latter. We are happy when we are active in pursuit of choice-worthy goals that we in some measure attain. On the other hand, there is no happiness without contentment, which requires the curtailing of ambition. There is thus a tension between two components of happiness. It is a tension between happiness as self-actualization and happiness as contentment.
To actualize oneself one must strive. One strives for what one doesn't have. Striving is predicated upon felt lack. But one who lacks what he desires is not content, not at peace, and so is unhappy in one sense of the term. One who longs for what is permanently out of reach will be permanently unhappy, always striving, never arriving. Not only will he not get what he wants, he will fail to appreciate what he has.
To be happy one must strive for, and in some measure attain, choice-worthy ends. That requires ambition. But the attaining is not enough; one must rest in and enjoy what one has attained. That requires the curtailing of ambition.