I think Courage is a way of being, and Authority is a way of communicating.
At least, I think I'm using "Authority" the way you are -- that is, not like power over, such as "I'm calling the authorities on you!" or even "He is the authority on courage!" .... but rather, the quality that has people's listening to what you say be very invested and accepting, such that the conscious faculty (the "bodyguard" that evaluates and judges, and keeps things from going straight in to your belief system) is lowered when you speak -- they are more suggestible to what you have to say because they trust it.
So, to increase your Authority, you'd probably want to work on communicating in such a way that people trust you, are in rapport with you, and are inclined to believe what you say and believe that you have their best interest in mind. To me, that involves being as aligned as possible with truth, and actually having the best interest of others in mind.
Not everyone agrees with that, though -- some people want and are able to develop authority while being wildly misaligned with truth and having very little interest at all in the well being of others. Which way you go depends on your values.