Green’s Dictionary of Slang

1. (Aus.) one who ‘fixes’ a situation, usu. through bribery (however well disguised).

1885		Bulletin (Sydney) 26 Sept. 6/4: [T]he day must come when the most expert of squarers can square successfully no longer, and there is an end even to the efficacy of hush-money.
1907		Lone Hand May 86: The suspicion of jockey-squaring [...] was not groundless [...] But Wren was also an unscrupulous ‘squarer’ of all sorts and conditions of men.
1931		(con. 1900s) C.W. Willemse Behind The Green Lights 101: What have you got there, a ‘squarer’?

2. something that helps sort out a problem.

1908

B. Fisher A. Mutt in Blackbeard Compilation (1977) 151: I’ll buy a bunch of violets as a squarer for the old lady.