Old English scearp "having a cutting edge; pointed; intellectually acute, active, shrewd; keen (of senses); severe; biting, bitter (of tastes)," from Proto-Germanic *skarpaz, literally "cutting" (source also of Old Saxon scarp, Old Norse skarpr, Old Frisian skerp, Dutch scherp, German scharf "sharp"), from PIE root *sker- (1) "to cut" (source also of Lettish skarbs "sharp," Middle Irish cerb "cutting").
The figurative meaning "acute or penetrating in intellect or perception" was in Old English; hence "keenly alive to one's own interests, quick to take advantage" (1690s). Of words or talk, "cutting, sarcastic," from early 13c. Meaning "distinct in contour" is from 1670s. The adverbial meaning "abruptly" is from 1836; that of "promptly" is first attested 1840. The musical meaning "half step above (a given tone)" is from 1570s. Meaning "stylish" is from 1944, hepster slang, from earlier general slang sense of "excellent" (1940). Phrase sharp as a tack first recorded 1912 (sharp as a needle has been around since Old English). Sharp-shinned attested from 1704 of persons, 1813 of hawks.