If the Tree is

a) Dead, or
b) Dangerous to persons, or
c) Dangerous to Property (ie fences, stormwater drains, sewerage drains, buildings, electricity service lines etc), or
d) Approved for removal under a Development Consent, or
e) is a Fire Hazard within a Fuel Free (Asset Protection) zone, is required to be removed pursuant to current Electicity Service Safety legislation then... LOPPING & REMOVAL IS PERMITTED WITHOUT COUNCIL APPROVAL. (Ref: Circular T1 of Snowy River Development Control Plan 1998.)

Otherwise a FREE Development Application (DA) is required to enable Environmental Assessment and appropriate Conditions of Development Consent to be imposed.
Tree Lopping & Removal DA usually takes less than 5 working days for determination if the application is properly made.
Tree Lopping & Removal form (at Council offices, online soon)