Some selected quotes from the Wikipedia page: https://en.wikipedia.org/wiki/New_Theatre,_Sydney

The New Theatre in Sydney is the oldest theatre company in continuous production in New South Wales.

Themes explored in the productions were mostly related to exploitation of the working class, sexism, racism in Australia, and against war.

[In 1936, both Sydney's New Theatre League and Melbourne's New Theatre] staged first Clifford Odets' play Waiting for Lefty, with the purpose of raising money for strikers, to great acclaim. With the rise of Nazism in Germany, then prepared to stage his play Till the Day I Die. After the German Consul General complained to the Commonwealth Government, the play was banned by Frank Chaffey, then Chief Secretary, but the theatre defied the ban and staged the play in private premises.

The Introduction page of their own wiki site gives a history of their various locations, as well as other cities which started similar projects, and their historical affiliations:

Sydney New Theatre is the sole survivor of similar groups which operated in Melbourne, Brisbane, Perth, Adelaide, Newcastle and Lithgow. At Easter 1939 Sydney played host to the first New Theatre League Conference (attended by Melbourne and Newcastle).

In the 1930s the organisation was affiliated with New Theatre USA, the British Drama League (BDL), the Workers' Educational Association (WEA), the Australian Youth Council, the Central Cultural Council of the Communist Party of Australia (CPA), and 15 trade unions.