Green’s Dictionary of Slang

stable v.

[stable n. (2)]

1. [1940s–50s] (Aus.) to be having an affair.

2. [1960s] (US) for a pimp to enroll a prostitute in his ‘team’.

In phrases

stable up (v.)

[1960s] (US black) of a prostitute, to join those girls working for a given pimp.