Green’s Dictionary of Slang

graduate n.

1. an up-market prostitute.

[UK]Partridge DSUE (1984) 493/2: a spinster skilled in sexual practice [...] from ca. 1885.

2. (also post-graduate) a clever, cunning man.

[UK]Partridge DSUE (1984) 493/2: from ca. 1875; ob.
Babs Gonzales ‘Manhattan Fable’ cited on ADS-L 7 June 2006 🌐 Freddie, being a post-graduate and a six-year New York man, knew the pig when he saw it.

3. (US Und.) one who has served a sentence.

[US]Hostetter & Beesley It’s a Racket! 226: graduate — One who has served a sentence in jail.
[US]L.E. Lawes Twenty Thousand Years in Sing Sing 75: My visit then was to check up the records of the prison to determine how many of our Reformatory ‘graduates’ had filtered into the big prison.
[US]Howsley Argot: Dict. of Und. Sl.
[US]L.J. Valentine Night Stick 240: Peter Colavecchio was holed up with ‘graduates’ of various penal institutions. There was Louis Scotti, Dave Bloom, and Tony Cutro, all of them two-time losers.