The most common and most likely answer to this crossword clue is the 11 letter word DOVETAILING
I've seen this crossword clue in The Sunday Telegraph
D
O
V
E
T
A
I
L
I
N
G
More clues leading to the result DOVETAILING
Buddy explains!

The straight part
We know that "Neatly fitting" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case neatly fitting = dovetailing.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 DOVETAILING mean?
DOVETAILING noun- The situation in which things are dovetailed.