Horayos 3:2-3

Horayos 3:2

If the Kohein Gadol or the king sinned after leaving office, then the former Kohein Gadol brings a bull (because he retains the same level of sanctity) but the former king proceeds as a private citizen.

Horayos 3:3

If the Kohein Gadol or the king sinned before taking office, they bring the offerings of private individuals. Rabbi Shimon says that if they became aware of their sins before taking office, they are liable to bring an offering but if they only became aware after taking office, then they are exempt.

We’ve been using the word “king” for clarity but the mishna actually uses the word “nasi” (ruler). At this point, the mishna clarifies that “nasi” refers to the king. Leviticus 4:22 says, “Should he commit one of the commandments of Hashem his God.” This means a ruler who is answerable to no one but God, i.e., the king (as opposed to a Tribal head).