Is the Republic primarily an ethical or political work? The central question of the book is whether or not justice is an inherently good virtue. Plato wants to show that justice benefits the soul. This question is an ethical question insofar as it concerns how people ought to act. Yet justice seems to be a political virtue. Justice appears to be both ethical and political.
On the one hand, any conception of justice includes a vision for how one ought to live one's life. Justice demands that certain responsibilities, obligations, and limits constrain the freedom of individuals. These constraints have ethical import; they specify how people should live. Thus virtue is an ethical concept.
On the other hand, justice only manifests itself in political settings. Justice occurs in cities, or, as Plato shows, in a soul which contains various factions within itself. In either case, justice concerns the ordering of parts, and so there is no need for it in unitary or solitary entities. Justice depends on plurality. Considered in this regard, justice must be a political concept, as it governs communal relationships and activities.
Consequently, justice is both ethical and political. It governs how people should live, and it does this in the political realm. Justice is a virtue, but it is a virtue that determines the ways in which multiple parties should interact with one another. To force the concept of justice into one category or the other would be to render the conception meaningless. Questions of justice are by nature connected to both ethics and politics.