The most common and most likely answer to this crossword clue is the 7 letter word INSULAR
I've seen this crossword clue in The Times
I
N
S
U
L
A
R
More clues leading to the result INSULAR
- Insult art endlessly? That’s narrow-minded
- Detached ulna is twisted over top of radius
- Keeping to oneself, sulk endlessly amidst dreadful rain
- Detached ruins scattered around US city
- After brief verbal abuse, a caller finally gets cut off
- Narrow-minded barb cut short by a Queen
- Endlessly malign a rally's leader, narrow-minded
- Urinals to be refurbished or withdrawn
- Remote city in ruins rebuilt
- Closed urinals in need of refurbishment
Buddy explains!

The straight part
We know that "Keeping to oneself" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case keeping to oneself = insular.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 INSULAR mean?
INSULAR noun- An islander.
- Of, pertaining to, being, or resembling an island or islands.
- Situated on an island.
- Separate or isolated from the surroundings; having little interaction with external parties; provincial.
- Having an inward-looking, standoffish, or withdrawn manner.
- Relating to the insula in the brain
- Relating to insulin