Max Weber argues that there are three types of authority. These are legal, traditional, and charismatic. I would argue that a leader can claim legal and charismatic authority or traditional and charismatic, but that a leader cannot really have both traditional and legal authority.
Legal authority is based on impersonal laws. This is the sort of authority that we have in modern societies. The president has power not because of his birth or because God gave him the right to govern, but because he was elected according to a set of laws. Those laws would equally have given the right to govern to anyone else who managed to defeat him in an election.
Traditional authority is based on the fact that things have always been done in a given way. People who have traditional authority typically have it because they have inherited it. There are few instances of this in modern society, but we could say that Kim Jong Un in North Korea holds power largely because his father and grandfather did before him. Outside of government, we could say that the Pope has this kind of authority.
Finally, charismatic authority is based on the particular attributes of the leader. A charismatic leader has the right to rule because he or she is particularly endowed with some important quality. Leaders of this sort exist mostly in organizations rather than in countries today. A person might claim authority to lead a megachurch, for example, because he or she is believed to be particularly holy or because he or she is particularly great at communicating their message.
Either legal or traditional authority can be asserted along with charismatic authority. Kim Jong Un can try to portray himself as someone with mystical qualities that make him a great leader. American presidents are often elected in part because people think they have superior qualities (and Donald Trump is essentially running his campaign on this idea). These leaders get part of their authority from each of these sources.
However, a leader cannot really have traditional and legal authority at the same time. These types of authority are incompatible as a person who rules by right of birth clearly did not get their mandate through impersonal laws.