The most common and most likely answer to this crossword clue is the 5 plus 3 letter word ONE’S OWN
I've seen this crossword clue in The Guardian
O
N
E
â
€
™
S
O
W
N
More clues leading to the result ONE’S OWN
Buddy explains!

The straight part
We know that "The Queen’s personal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the queen’s personal = one’s own.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.