The most common and most likely answer to this crossword clue is the 11 letter word PREROGATIVE
I've seen this crossword clue in The Times
P
R
E
R
O
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T
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More clues leading to the result PREROGATIVE
Buddy explains!

The straight part
We know that "Right" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case right = prerogative.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 PREROGATIVE mean?
PREROGATIVE noun- A hereditary or official right or privilege.
- A right, or power that is exclusive to a monarch etc, especially such a power to make a decision or judgement.
- A right, especially when due to one's position or role.
- A property, attribute or ability which gives one a superiority or advantage over others; an inherent advantage or privilege; a talent.
- Having a hereditary or official right or privilege.