The rules regarding tree removal differ from council to council, but the State Environmental Planning Policy (Biodiversity and Conservation) 2021 and Development Control Plans (DCPs) guide many of the decisions made.
You should seek advice from your local council prior to removing any tree(s) from your property. You may need to obtain a permit or approval to remove the tree(s). Failing to do so can incur substantial fines.
If you live close to bushland or in an area that is prone to bushfires, check the 10/50 vegetation clearing entitlement area.
If your property is located in a designated area, the 10/50 Vegetation Clearing Scheme allows you to clear certain vegetation near your home without having to get approval from the local council or land services office.
Note: If you have a NSW Planning Portal account you may be able to apply for a Private Tree Permit via the Portal. Check if your council receives Planning Portal applications, as not all do.