I don't think I would use a priori or a posteriori here; I generally hold that wisdom is based on understanding, not on knowledge.
For a somewhat trite analogy, consider that we can gain a tremendous amount of 'knowledge' about how a baseball is thrown by studying bones, muscles, and neurons. But all of that knowledge is tangential to the act of picking up a baseball and throwing it. When we pick up a baseball and throw it, we 'understand' the act in a way that doesn't rely on formal knowledge at all. We're obviously not born with the ability to throw a baseball, but we also don't 'learn' it in our high school physics classes.
Wisdom as it's typically understood operates in much the same way. But rather than being an organic biophysical understanding, it's an organic moral or sociological understanding. We come to understand what to do as we develop our innate humanness; we don't have to work it out in some intellectual fashion.