The most common and most likely answer to this crossword clue is the 10 letter word FRANCHISEE
I've seen this crossword clue in The Times
F
R
A
N
C
H
I
S
E
E
More clues leading to the result FRANCHISEE
Buddy explains!
The straight part
We know that "One with specific rights" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one with specific rights = franchisee.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 FRANCHISEE mean?
FRANCHISEE noun- A holder of a franchise; a person who is granted a franchise.