Green’s Dictionary of Slang

(US) a drink in a tavern; thus enter a plea, to order a drink.

1848		‘Ned Buntline’ Mysteries and Miseries of N.Y. I 115: ‘Plea at the bar.’ Taking a drink.
1848		‘Ned Buntline’ Mysteries & Miseries of NY 16: ‘[L]et’s walk up to the bar and enter a plea, boys; I’ve had my fun, and it’s my treat’.