Green’s Dictionary of Slang

1. ‘fashionable Slang for a brougham, or other private carriage’ (Hotten, 1859).

1853		Dickens ‘Slang’ in Household Words 24 Sept. 77/1: A vehicle which is not a drag (or dwag) is a ‘trap’ or ‘cask.’.
1863		Story of a Lancashire Thief 11: I’ve heard him talk slang like a professional. Once I heard him telling two chums of his about tooling his drag to the Derby; in fact he knew all about traps, and casks, and drags, and rounders.
1873		Sl. Dict.

2. (US Und.) a taxi.

1935

A.J. Pollock Und. Speaks 19/1: Cask, a cab or taxi.