He has a hank on him; i.e. an ascendancy over him, or a hold upon him. A Smithfield hank; an ox, rendered furious by overdriving and barbarous treatment. See Bull Hank.
Definition taken from The 1811 Dictionary of the Vulgar Tongue, originally by Francis Grose.
See also the definition in Nathan Bailey's 1736 dictionary of canting and thieving slang.
Hangman’s Wages * HankerNathan Bailey's 1736 Dictionary of canting and thieving slang
John S. Farmer's collection of canting songs and slang rhymes