The most common and most likely answer to this crossword clue is the 3 letter word WHO
I've seen this crossword clue in The Times
W
H
O
More clues leading to the result WHO
- International organisation's question of identity
- Personal question from health authority
- Question authority
- Which people? The ones advising on our wellbeing
- Alien doctor in UN health agency
- Which one of us is a doctor?
- Place for VIPs to show off — and how!
- Sex won’t start to help terribly – it’s someone else’s turn!
- Which person’s essential know-how
- Question leader in White House
Buddy explains!

The straight part
We know that "Personal question" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case personal question = who.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 WHO mean?
WHO noun- A person under discussion; a question of which person.
- (interrogative) What person or people; which person or people; asks for the identity of someone. (used in a direct or indirect question)
- (interrogative) What is one's position; asks whether someone deserves to say or do something.
- (relative) The person or people that.
- (relative) Whoever, he who, they who.