Green’s Dictionary of Slang

a worn-out shirt.

1844		Tipperary Free Press 29 June 2/6: He was dressed [in] a pair of nondescript unmentionables and a calico breast-plate vulgarly y’clept a tommy.
1860		Hotten Dict. of Modern Sl. etc. 238: Tommy ― See DICKEY [i.e. ‘a worn out shirt, but means, now-a-days, a front or half-shirt’].
1873		Sl. Dict.
1895		Crowe Aus. Sl. Dict. 87: Tommy, a detatched shirt front.