Old English scearp "cutting, keen, sharp," from Proto-Germanic *skarpaz, literally "cutting" (cf. Old Saxon scarp, Old Norse skarpr, Old Frisian skerp, Dutch scherp, German scharf "sharp"), from PIE *(s)ker- "cut" (cf. Lettish skarbs "sharp," Middle Irish cerb "cutting;" see shear). The figurative meaning "acute or penetrating in intellect or perception" is from Old English. The meaning "promptly" is first attested 1840. The musical meaning "half step above a given tone" is from 1570s. Phrase sharp as a tack first recorded 1912 (sharp as a needle has been around since Old English).
"a cheat at games," 1797, short for sharper (1681), probably a variant of sharker (see shark). Meaning "expert, connoisseur" is attested friom 1840, and likely is from sharp (adj.).