Both versions are grammatically correct and natural, but they have different nuances. Which one is correct depends on context that I don't know.
Here, an has the normal meaning of "one among many", and simply expresses that this person has done many appearances, but this is their first time specifically doing an appearance as a star of Lion King.
In contrast, any strongly emphasizes that this is the really their first time, and they have never done such an appearance before. This level of emphasis is only used when it should surprise the listener that this is the first time.
So, if the movie just came out, it shouldn't surprise anyone that this is their first appearance, and only "an" works.
But if they movie came out years ago, it would be quite surprising that they hadn't made an appearance since then, so "any" works much better, though "an" is still grammatically correct.