The most common and most likely answer to this crossword clue is the 8 letter word TASMANIA
I've seen this crossword clue in Financial Times
T
A
S
M
A
N
I
A
More clues leading to the result TASMANIA
- Brooded over craze for place roamed by devils?
- Island placed to the west has overly excited state
- State expressions of gratitude: an obsession
- Satan with aim to create Devil's Island?
- Island like isle in Taiwan, oddly
- Qantas man I approached, crossing part of Australia
- Tense Australian male entering troubled Asian island state
- Island in Fantasia? There’s no cooler island
- Australian territory
- Settled to reject obsession for overseas state
Buddy explains!

The straight part
We know that "part of Australia" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of australia = tasmania.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.