The most common and most likely answer to this crossword clue is the 3 letter word OWN
I've seen this crossword clue in The Times
O
W
N
More clues leading to the result OWN
- What’s now horribly personal
- Private heading away from urban area
- Have time away from built-up area
- Admit wife into cricket side
- Keep climbing Snowdon on a regular basis
- Have blue cap missing
- Private cricket side hosting Worcestershire’s opener
- Keep wrapper from butter, with or without manufacturer’s label?
- Have to admit it hurt so close to recognition
- Have some tomorrow night
Buddy explains!

The straight part
We know that "Private" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case private = 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.
What does OWN mean?
OWN adjective- Belonging to; possessed; proper to. Often marks a possessive determiner as reflexive, referring back to the subject of the clause or sentence.
- Not shared
- Peculiar, domestic.
- Not foreign.
- To have rightful possession of (property, goods or capital); to have legal title to.
- To have recognized political sovereignty over a place, territory, as distinct from the ordinary connotation of property ownership.
- To defeat or embarrass; to overwhelm.
- To virtually or figuratively enslave.
- To defeat, dominate, or be above, also spelled pwn.
- To illicitly obtain superuser or root access to a computer system, thereby having access to all of the user files on that system; pwn.
- To grant; give.
- To admit, concede, grant, allow, acknowledge, confess; not to deny.
- To admit; concede; acknowledge.
- To take responsibility for.
- To answer to.
- To recognise; acknowledge.
- To claim as one's own.
- To confess.