strap, n.⁴ — Green’s Dictionary of Slang

strap n.⁴

[the SE strop used to sharpen razors. Note Hugh Strap, a barber, in Tobias Smollett’s Roderick Random (1748)]

a barber.

1864, 1867, 1870		Hotten Sl. Dict.
1873		Sl. Dict.
1882		Sydney Sl. Dict. (2 edn) 11: Strap - A barber (from ‘Roderick Random’).
1890–1904		Farmer & Henley Sl. and Its Analogues.