early 14c., wrappen, "to wind (something around something else), cover (something), conceal; bind up, swaddle; fold (something) up or back on itself," of uncertain origin, perhaps via Scandinavian (compare Danish dialectal vravle "to wind"), from PIE *werp- "to turn, wind," from root *wer- (2) "to turn, bend." Or perhaps a variant of lap (v.2). To wrap up "put an end to" is from 1926. Related: Wrapped; wrapping. Wrapping paper is from 1715.
c. 1300, "in circumference, in a circle, on every side," from phrase on round; see a- (1) + round (adj.). It was rare before 1600. In the sense of "here and there with no fixed direction" it is attested from 1776 in American English (British English prefers about).
As a preposition, "on or along a circuit," from late 14c.; "on all sides, encircling, about" from 1660s; of time, by 1873. To have been around "gained worldly experience" is from 1927, U.S. colloquial; to get around to it is from 1864.
<a href="https://www.etymonline.com/word/wraparound">Etymology of wraparound by etymonline</a>
Harper, D. (n.d.). Etymology of wraparound. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/wraparound