Plato and many other Classical authors were members of the leisure class. They owned enough property - in the form of land, houses, workshops, mining concessions, slaves, or all of the above - to be able to get by without doing any paid work. They were philosophers (the word means "lover of knowledge"), which is to say that they were engaged in the disinterested pursuit of knowledge and wisdom for its own sake. From Plato onward, this pursuit was distinguished sharply from that of the so-called sophists (which we may tendentiously translate as "know-it-all"), who hired themselves out as teachers of particular skills or scientific fields. In Plato's eyes, the sin of the sophists was precisely that they charged money for their knowledge. Learning, in his view (as well as the view of Sokrates), was supposed to be for all who hungered for it, not just for those who could pay.

Because of this moral commitment to philosophy, it was unthinkable for someone like Plato to try to use what he had learned for monetary or political gain. Sophists charged money for lectures, taught rhetoric, and served their home states as orators and ambassadors; the "true" philosopher did none of these things.

For this reason, Plato, as well as Sokrates and authors like Thucydides and Xenophon, cannot possibly fit within the role of any modern job. They were specifically and deliberately neither professors (if such a thing may be said to have existed) nor politicians. They were independent scholars, who taught mostly interested members of their own social network, but also had an international reputation that attracted students from far and wide. I don't think there is an equivalent to this role in modern society.