Interesting question, thank you Chloe-Jane. The Governor-General is appointed by the Queen on the advice of the Prime Minister. The Governor-General’s appointment is at ‘the Queen’s pleasure’, that is, without a fixed term. In practice, most appointments are for around five years. Sometimes this term is extended.
A Governor-General can be dismissed by the Queen before their term is complete. By convention (tradition), this may only be on the advice of the Prime Minister. No Governor-General has ever been dismissed.
If a Governor-General was dismissed, a vacancy would then occur, just as it does when a Governor-General resigns (this has happened three times). Section 4 of the Australian Constitution allows the Queen to appoint an administrator to carry out the role of Governor-General when there is a vacancy. The longest-serving state governor would take on the role of Governor-General until the position can be permanently filled.
Find out more about the role of the Governor-General with this fact sheet.