outskirt (n.)

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

early 14c. (mid-13c. as a surname), "lower part of a woman's dress," the part that hangs from the waist, from Old Norse skyrta "shirt, a kind of kirtle;" see shirt, which is from the Old English cognate, and from which it is not always distinguishable in early use.

The sense development from "shirt" to "skirt" is obscure; it could be from the long shirts of peasant garb (compare Low German cognate Schört, in some dialects "woman's gown").

Also "lower part of a man's gown, clerical vestment, etc." (late 14c.). The sense of "border, edge, part of anything furthest from the mass or the center" (in outskirt, etc.) is recorded by late 15c.

Metonymic use for "women collectively" is from 1550s; the slang sense of "young woman" is from 1906; skirt-chaser is attested by 1942.