go, n.³ — Green’s Dictionary of Slang

go n.³

give someone/something the go (v.) [abbr. give someone/something the go-by under go-by n.] (Aus./N.Z.)

1. to reject a suitor.

1904		‘G.B. Lancaster’ Sons O’ Men 231: ‘Give you the go, ’as she?’ he asked delicately.
1988		McGill Dict. Kiwi Sl. 50/1: give the go to reject a suitor or abandon a place or job; short for ‘give the go-by’; eg ‘Why don’t we give this game the go, eh?’.
2003		McGill Reed Dict. of N.Z. Sl. [as cit. 1988].

2. to give up a job, leave a country etc.

1988, 2003

see sense 1.