Green’s Dictionary of Slang

(Aus.) a well-known individual, usually a local ‘character’, eccentric or (petty) criminal .

1860		Golden Age (Queanbeyan, NSW) 27 Oct. 2/1: [T]he return of even an ‘unknown’ like Mr Brackenbury would be more creditable than the election of ignorance and presumption that may have attained to the eclat of a local notoriety.
1869		Geelong Advertiser (Vic.) 19 Feb. 3/: Margaret Healey, convicted of stealing money from ‘Joe the bellman,’ a local notoriety, was sentenced to four months’ imprisonment. The prosecutor in this case is an eccentric individual; and the characteristic manner in which he delivered his evidence caused frequent bursts of laughter.
1878		Williamstown Chron. (Vic.) 19 Oct. 2/3: On Tuesday a local notoriety named Peggy Jones was sent to gaol [...] as a vagrant. [...] Peggy has been convicted nearly fifty times at the local Court, her prominent appearances being 28 for drunkenness, 8 for obscene language, 4 for vagrancy, and 2 for larceny.
1881		Melbourne Punch 27 Jan. 7/3: A country paper, writing the obituary of a local notoriety, pens the following paragraph pregnant with meaning:—‘The deceased [...] was esteemed by all who knew him as a good citizen and a worthy man, for his character was unspotted [...] though in former years he had been an attorney.
1897		Maitland Dly Mercury 2/5: [A] local notoriety, one D. T. Trimm, took on the printer's devil in a match for £50 over 160 yards and had to play second fiddle.
1902		Tocsin (Melbourne) 17 July 6/2: Since Yarra-bank Agitator Fleming has fraternised with vice-royalty, he is becoming quite a notoriety among ‘respectable people’ .
1912		Telegraph (Brisbane) 13 Apr. 2/5: [A] local ‘notoriety’ named Biddy Byrne, who was summoned for being drunk, said: ‘Oh, your worship, sure I am just after coming from Father Delancy, this blessed minute, and he says whatever the court wishes he will do it for me’ .
1923		Mercury (Hobart, Tas.) 19 Sept. 5/3: Jack Trent opening at the Bijou Theatre on Saturday is quite a notoriety in sporting circles.
1931		Arrow (Sydney) 27 Nov. 4/1: Bill Jones is quite a notoriety in the neighborhood. He is a liar, a thief, and [...] is not above trying a bit of thuggery. The community knows him as a ne’er-do-well, the police as the one most likely to have a hand in the latest robbery.
1946		West Australian (Perth) 3 Aug. 5/5: This is reminiscent of the early days at Black Range in Western Australia and of a local notoriety, the Mulga Queen, who conducted a beer shanty. She was a repulsive, untidy creature with a hard face and a foul tongue.