Office of Environment & Heritage states;
'All native birds, reptiles, amphibians and mammals (except the dingo) are protected in NSW by the Biodiversity Conservation Act 2016 (BC Act).' This covers; culling, catching and releasing.
Exceptions or limits to the protection of native animals Some native birds are not protected in certain parts of NSW because they are either agricultural or pastoral pests:
Sulphur-crested cockatoos and galahs have been declared 'locally unprotected' in the Western, North West, Central West, Riverina and Murray Local Land Services regions (excluding national parks and conservation areas), because of the damage they do to grain and oilseed crops
Crows and ravens (corvids) are protected only in Greater Sydney Local Land Services region (and national parks and conservation areas), because they are blamed for the deaths of lambs in other areas.
Purple swamphen is not protected in 10 irrigation districts and areas in the Riverina and Murray Local Land Services regions (excluding national parks and conservation areas), where the species causes considerable damage to irrigated crops such as rice.
If you need to dive in deeper, here is the website for the Office for Environment & Heritage