Prudence, indeed, will dictate that governments long established should not be changed for light and transient causes . . how does the author appeal to ethos here? (apex btw)

An appeal to ethos is an appeal to credibility or moral character. It is a type of persuasive argument, which means that it attempts to convince an audience of a particular argument. In this case, the author is telling us that governments that have a long standing tradition are usually managed by "prudent" (careful, wise) people, which means that they do not often change for unimportant or temporary reasons.

c hope this you