(1):

(v. t.) To provide, as a shoe, with new upper leather; hence, to piece, as any old thing, with a new part; to repair; to patch; - often followed by up.

(2):

(n.) The part of a boot or shoe above the sole and welt, and in front of the ankle seam; an upper.

(3):

(n.) Any piece added to an old thing to give it a new appearance. See Vamp, v. t.

(4):

(v. i.) To advance; to travel.