In his influential work, De Officiis, Ambrose of Milan argues that modestia is one of the most important duties/responsibilities (officiis) of youth; he takes it to be the restraint of oneself in word and action, giving as examples chastity, humility, sobriety, silence, and the like. One of the kinds of modestia he notes is that concerned with gesture and gait of body:
Modesty must further be guarded in our very movements and gestures and gait. For the condition of the mind is often seen in the attitude of the body. For this reason the hidden man of our heart (our inner self) is considered to be either frivolous, boastful, or boisterous, or, on the other hand, steady, firm, pure, and dependable. Thus the movement of the body is a sort of voice of the soul.
Since there is an intimate relation between our bodies and our souls, there is a relationship between our outward movement and our character, with the former serving as a sign of the latter. Ambrose is rather brutal in his assessment; he gives specific examples of people he has known who showed their arrogance or faithlessness in how they walked and moved their hands. One of the Ambrose's concerns is our tendency to posture and preen, to treat our body as if it were a way to manipulate other people. Another is that our lack of priorities often shows up in how we move -- our hastiness, our self-importance, our lack of respect for ourselves and our position. Our movements should be simple and plain, appropriate to our situation and our station, communicating the spiritual beauty of our characters through the natural ease and dignity of our use of our bodies. Conceit and deceit, arrogance and artifice, are especially to be avoided.
Aquinas follows Ambrose in accepting that there must be such a virtue (2-2.168.1), again, because denying that morality includes this sort of thing in its scope is to falsify the relationship between soul and body. Morality is concerned with the direction of action by reason; and our physical movements are directions capable of being directed by reason. Thus there is a virtue of moving rationally. It is a subjective part (particular kind) of modestia, which is a potential part (close cousin) of temperance -- the difference being that temperance, the more important virtue, is concerned with internal matters.
There are two things we need to keep in mind in order to achieve this modestia of movement: we need to make our movements appropriate to the people with whom we deal (including ourselves), and we need to make our movements appropriate to the situation in which we find ourselves. Thus Aquinas identifies two elements to this moderation of external movements: ornatus, which concerns the former, and bona ordinatio, which concerns the latter. (He gets the terms from Andronicus of Rhodes.)
This all might sound a bit odd as a matter of ethics, and again, we have no actual word in English to describe the virtue in question. However, a little thought shows that there must be something to it. One of our most basic notions of 'good behavior' consists entirely in the kind of moderation of physical movement covered by good behavior. We see this especially in how we train children, but we occasionally express the same sort of approval and disapproval in how we regard adults, and our annoyance and social penalizing of jostlers, those who invade people's personal space or take up more room than they need to, those who rush around, those who flail wildly, those who cannot keep their hands to themselves. And it is unsurprising, really: how we move is one of our forms of communication, and we get exasperated at people who move in such ways that they act as if they were the only person who mattered, or as if they were trying to dominate others or the situation. Like Ambrose, most people recognize that you can move in ways that force others to adapt and that communicate exactly the wrong things; and, like Ambrose, most people get exasperated at the kinds of outward movements suggestive of arrogance or pretense. Nobody, whether Ambrose or Aquinas or anyone else, considers the virtue in question to be among the most important virtues; but that there is something about moral life involved can hardly be put into question.