Green’s Dictionary of Slang

(UK Und.) a gambler, presumably a cheat, who wins.

1608		Dekker Lanthorne and Candle-Light Ch. 3: He that winnes all, is the Eagle.
1685		New plot newly discovered 4: The Forlorne-Hope doth gallantly come on, the Eagle feathers his nest, the Wood-pecker picks up his crumbs, the Gull-groper grows fat [...] and the Gull himself [has] scarce enough to keep his back warm .
c.1698		B.E. Dict. Canting Crew n.p.: Eagle c. the winning Gamester.
1725		New Canting Dict. [as cit. c.1698].
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. c.1698].