Green’s Dictionary of Slang

1. (US) a resumption of relations after a falling-out.

1896

F. Hutcheson Barkeep Stories 150: ‘It’s sure all off wid me an’ him now an’ no chance fer a square-up’.

2. (Aus.) a fight, an argument.

1985		R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 22: Any ideas he had about a sneak square-up with Norton he could forget.
1986		R.G. Barrett Godson 90: Les could detect from the tone of his voice there might be a bit of a square up coming.

3. (Aus.) a settlement of scores, a payment of lit. or fig. debts; also attrib.

1985		R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 179: Most blokes who had just been four-outed would probably start putting the boot in for a bit of a square-up once they got on top.
1998		R.G. Barrett Mud Crab Boogie (2013) [ebook] [T]hey jumped in the cousin’s car and come [sic] back for a square up knowing four of them could give it to him easy.
1999		R.G. Barrett Wind & Monkey (2013) [ebook] Now they’d have two cops hanging around for a piddly, square-up pot bust.
2000		R.G. Barrett Leaving Bondi (2013) [ebook] ‘Then there definitely has to be a square up.’ ‘Oh! A square up for sure, mate’.
2012		(con. 1943) G.S. Manson Coorparoo Blues [ebook] ‘Special Branch had him for a load of the stuff in a garage, and it was offered to him as a square-up deal’.