Days after proclaiming harsh new anti-protest laws, the NSW government has intervened in a High Court challenge to similar Tasmanian laws by former Australian Greens leader Bob Brown.

A notice filed to the High Court on Monday by Crown Solicitor Michael Sexton reveals NSW Attorney-General Gabrielle Upton is seeking to support the Tasmanian government.

In January, Mr Brown was among five people charged under Tasmanian anti-protest laws while protesting the logging of 49 hectares of the Lapoinya forest in the state's north-west.

Police later dropped the charges but Mr Brown and another protester, nurse Jessica Hoyt, are pursuing their legal challenge against the laws, designed to prevent the disruption of mining and forestry projects.