The most common and most likely answer to this crossword clue is the 9 letter word TASMANIAN
I've seen this crossword clue in The Guardian
T
A
S
M
A
N
I
A
N
More clues leading to the result TASMANIAN
- Antipodean army’s obsession with north
- Islander from a small island, one with brown skin?
- Aussie Brown entertains primarily sexual obsession
- Antipodean army chap embraced by Welsh girl
- Islander thanks Welsh girl entertaining crew
- Dutch heart and soul in continental islander
- Southern islander is man with a tan, possibly
- Islander in court as man I antagonised
- Ceaseless work with passion by North Australian
- Islander cheers Welsh girl entertaining crew
Buddy explains!

The straight part
We know that "islander" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case islander = tasmanian.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.