Green’s Dictionary of Slang

tie up v.1

[the image of tying up one’s villainy and putting it away]

(UK Und.) to abandon, to give up, e.g. tie up prigging, to give up one’s criminal life, to become honest.

[UK]Foote Minor in Works (1799) I 241: I have a great mind to tie up, and ruin the rascals.
[Aus]Vaux Vocab. of the Flash Lang. in McLachlan (1964) 277: To tye it up is a phrase, which, used emphatically, is generally understood to mean quitting a course of depredation and wickedness.
[UK]Pierce Egan’s Life in London 13 Aug. 645/1: [of a boxer] Dick Curtis wishes to have another trial of skill before he ‘ties-up’.
[UK]H. Brandon ‘Dict. Flash or Cant Lang.’ in ‘Ducange Anglicus’ Vulgar Tongue (1857) 37: Tied up prigging given over thieving.
[UK]‘Ducange Anglicus’ Vulgar Tongue.
[Aus]Crowe Aus. Sl. Dict. 85: Tied Up Gonnoffing, reformed, living honestly.
[US] ‘West Point Sl.’ in Howitzer (US Milit. Academy) 292–5: Tie-up — To bungle; to make a failure of.