What became of the aristocrats when kings no longer ruled greek city-states?

Well, depending on the individual city states, a couple different things could have happened. In some city states, the aristocrats themselves took power, and formed oligarchies, which are forms of government in which small groups of upperclassmen control the city state. Sometimes a tyrant would take over after a king, and the aristocrats would either stay aristocrats and advisors to the king, or be pushed down to lower class citizens as time went on to be replaced by other advisors the tyrant favored better. In Athens, the aristocrats would remain wealthy citizens when the democracy began (as a rule), but they would no longer rely solely on politics to provide for them.