To gain on ∨ upon Meaning, Definition & Usage

Definitions
  1. . (a) To encroach on; as, the ocean gains on the land. (b) To obtain influence with. (c) To win ground upon; to move faster than, as in a race or contest. (d) To get the better of; to have the advantage of.
    The English have not only gained upon the Venetians in the Levant, but have their cloth in Venice itself. Addison.

Webster 1913