Green’s Dictionary of Slang

to have the advantage over, the implication is of potential blackmail.

c.1698		B.E. Dict. Canting Crew n.p.: He has a Hank upon him, or the Ascendant over him.
1725		New Canting Dict. n.p.: He has a Hank upon him; He has an Advantage, or will make him do what he pleases.
1737, 1759, 1760, 1776		Bailey Universal Etym. Eng. Dict. [as cit. 1725].
1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue.
1811		Lex. Balatronicum.
1812		Vaux Vocab. of the Flash Lang. in McLachlan (1964) 245: hank: to have a person at a good hank, is to have made any contract with him very advantageous to yourself; or to be able from some prior cause to command or use him just as you please; to have the benefit of his purse or other services, in fact, upon your own terms.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.
1859		Matsell Vocabulum 40: hank To know something about a man that is disreputable. ‘He has a hank on the bloke whereby he sucks honey when he chooses,’ he knows something about the man, and therefore induces him to give him money when he chooses.