The most common and most likely answer to this crossword clue is the 8 letter word ZANZIBAR
I've seen this crossword clue in Independent
Z
A
N
Z
I
B
A
R
Buddy explains!
The straight part
We know that "island group of 13" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case island group of 13 = zanzibar.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.