The following sentence is ambiguous. Provide two explanations which illustrate the different meanings of the sentence. "We need more empathetic leaders."

The key word here is the adjective “more.” Does it modify “empathetic,” or does it modify “leaders?”
If “more” modifies the adjective “empathetic,” then it indicates the degree of the emotion. The sentence would refer to the fact that we need leaders who are more empathetic, more understanding, more compassionate, and more connected to us followers and to the situations that we are experiencing. The leaders need to imagine themselves in our shoes sometimes, in order to understand what’s going on with us.
If “more” modifies the noun “leaders,” then it merely indicates quantity. Yes, we do indeed need leaders who are understanding, compassionate, and connected; but we need more of these people than we already have. The implication is that we already have a few of these kinds of leaders; but we don’t yet have enough of them. At least, not in the speaker's opinion.