Old English impe, impa "young shoot, graft," from impian "to graft," probably an early Germanic borrowing from Vulgar Latin *imptus, from Late Latin impotus "implanted," from Greek emphytos, verbal adjective formed from emphyein "implant," from em- "in" + phyein "to bring forth, make grow," from PIE root *bheue- "to be, exist, grow." Compare Swedish ymp, Danish ympe "graft."
The sense of the word has shifted from plants to people, via the meaning "child, offspring" (late 14c., now obsolete), from the notion of "newness." The current meaning "little devil" is attested from 1580s, from common pejorative phrases such as imp of Satan. The extension from this to "mischievous or pert child" (1640s) unconsciously turns the word back toward its Middle English sense.
Suche appereth as aungelles, but in very dede they be ymps of serpentes. [Wynkyn de Worde, "The Pilgrimage of Perfection," 1526]