Green’s Dictionary of Slang

1. (US) a regular customer.

1953

W. Fisher Waiters 16: He knew the people who came day in and week out [...] the ‘steadies,’ as the waiters called them.

2. (US) a prostitute’s regular customer.

1960		‘Lord & Marshall’ Girl Called Honey 54: She [i.e. a prostitute] thought that Madge would be disappointed when she didn't show up at the house the following day [...] and that some of her steadies would grumble when they discovered she was literally nowhere to be had.
1961		T.I. Rubin In the Life 112: If there’s a chance of making a John a steady, you know, a regular customer, I don’t want to louse it up.
1994		R.P. McNamara Times Square Hustler 39: Although Raul has fewer clients, almost all are ‘steadies’.