At first sight it looks like there is little room for aesthetics in the debate between Socrates and Thrasymachus. However I have a somewhat broader, one might even say expansive, notion of aesthetics than most. We have to consider first that the concept of craft and craftsmanship is central to this debate over the nature of justice. The ancient Greeks did not have a word that translates well to our word "art," but it is commonly believed that techne comes closest, and this is the word that is commonly translated as "craft." After Thrasymachus gives his definition of justice as whatever is in the interests of the stronger, and understands the stronger in terms of those who are in power in a particular society, whether it be a tyrant or "the many," he is confronted by Socrates with the problem that the ruler may not know what his own interests are and thus that the ruler might unintentionally order what is bad for himself. Thrasymachus, in a surprisingly sophisticated and momentous move, insists that someone who is in error is not stronger at the very moment he makes a mistake. The subtle point is that a doctor is not, strictly speaking, a doctor when he makes a mistake in doctoring: when someone makes an error in the treatment he is not called a doctor "in virtue of the fact that he made that very error." To the extent that the craftsman in that craft is a doctor or a horse-trainer, etc., he never makes errors.
Now, strictly speaking, this is false, and there is no immediately obvious reason why Socrates should have gone along with Thrasymachus on this point. We continue to call doctors doctors even when they make mistakes! Why should we abandon that custom? Obviously someone can make a mistake as a doctor. The only way to save this would be to say that he is not an ideal doctor. Yet to say that someone is not a doctor if that person is not an ideal doctor seems the worst form of Procrustean idealism, a kind of naive form of Platonism, perhaps based on the mathematical analogy that something is not a circle if it is not an ideal circle (and that everything called a circle in the world of appearance is not really a circle simply because nothing in our world can have all of its points equidistant from the center).
But there is a deeper point involved here (so maybe I was wrong that there is only one way to save it.) Socrates goes along with this innovation because it fits nicely with his preconceptions about the crafts and it allows him to insist that a doctor is a doctor in the strict sense not when he is a moneymaker, for example, but when he is someone who treats the sick. Similarly, a ship's captain is such not because he is someone who sails but because he rules over sailors in such a way as to effectively sail. Thus, in general, (and this would apply to what we call the craft arts and the fine arts as well) "the natural aim of the craft is to consider and provide what is advantageous" for the craft in question. Moreover, Socrates argues, what is advantageous is to "be as perfect as possible." Socrates explains that a craft like medicine does not need some further virtue nor does it need some further craft to determine what is advantageous to it. It considers "by itself" what is advantageous for it. In short, it is "without fault ...so long as it is wholly and precisely the craft that it is." And so, because of this, "medicine does not consider what is advantageous for medicine, but for the body."
Similarly, one could say that painting, as a craft, does not consider what is advantageous for painting but for its object, whatever it is that is the function of painting, i.e. "that with which it deals." (It is hard to specify what this is!) So, the crafts "rule over" their objects and yet not for their own advantage, thus refuting Thrasymachus' theory of justice using his own idea of perfection in a craft. Similarly a knowledge which attaches to a craft is not concerned with what is advantageous to itself but to what is subject to it. Qua doctor, the doctor is going to be concerned with the advantage of the patient. The question now then, for the fine arts, would be what the patient is. This would also all go against the idea that painting should only be about the success of the painter or about the success of painting itself, or even about painting itself.
So from Plato's perspective the arts, including the fine arts, would be aiming for the advantage of their subjects just as does any other craft, and that painting, for example, is not at fault as long it is wholly the craft that it is, and as long as it satisfies its function, whatever that is. Of course Plato later rejects the imitative arts from the ideal society, but at least we have an idea of such arts here as each having its own virtue and function, each being in a certain sense autonomous, each involved with self-perfection, each concerned with improving its subject, whatever that is.