The most common and most likely answer to this crossword clue is the 11 letter word UNCLUTTERED
I've seen this crossword clue in The Guardian
U
N
C
L
U
T
T
E
R
E
D
Buddy explains!

The straight part
We know that "Neat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case neat = uncluttered.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 UNCLUTTERED mean?
UNCLUTTERED verb- To eliminate clutter from.
- To eliminate clutter.
- Not cluttered; without clutter