The most common and most likely answer to this crossword clue is the 8 plus 7 letter word GOVERNOR GENERAL
I've seen this crossword clue in The Times
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More clues leading to the result GOVERNOR GENERAL
Buddy explains!

The straight part
We know that "Crown representative" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case crown representative = governor general.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.
What does GOVERNOR GENERAL mean?
GOVERNOR GENERAL noun- An official appointed by the reigning British monarch to govern a Commonwealth realm as the monarch's representative.
- An official in a similar position in other countries.
- A zongdu.