They suddenly became [by no wish of their own] both important and renowned (1),
and [they] troubled the counsels of the Wise and the Great (2).
As you correctly pointed out, trouble can be a verb and it's the role it plays in this passage. It's presented in the past simple form. It's a regular verb, thus trouble - troubled - troubled.
When you trouble (verb) someone, you cause them trouble (noun).
In our sentence, they troubled the counsels. Counsels are basically people you go to in order to receive some piece of advice (or, to put it old-fashionedly or formally, counsel). Nowadays, counsel is usually used to refer to a layer who gives legal advice or/and takes part in legal cases.
Moreover, they troubled the counsels of the Wise and the Great. Counsels tend to be highly intelligent and competent because they are expected to provide their "clients" with sound and valuable advice on complicated matters. And of the Wise and the Great is just a nice old-fashioned way to emphasise that, to stress that even exceptionally wise and highly regarded members of society were troubled by them.