The most common and most likely answer to this crossword clue is the 8 letter word PROSPERO
I've seen this crossword clue in The Times
P
R
O
S
P
E
R
O
More clues leading to the result PROSPERO
- True love overwhelms singular stage hero
- Rich American abandoned the rightful Duke of Milan
- Magician on island, rich, having abandoned US
- Flourish given by ordinary Shakespearean character
- The Duke of Milan’s quite correct to defend son, Oscar
- Shakespeare’s one spelling ‘fare well’ at end of Othello
- Son seen in genteel circle
- Magician‘s power shortening both names of one-time presidential candidate
- Magician puts sulphur in right hole
- Exiled king needs to get on well, having nothing
Buddy explains!

The straight part
We know that "Magician on island," is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case magician on island, = prospero.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.