The most common and most likely answer to this crossword clue is the 9 letter word OBSESSIVE
I've seen this crossword clue in The Times
O
B
S
E
S
S
I
V
E
Buddy explains!

The straight part
We know that "Neurotic" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case neurotic = obsessive.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 OBSESSIVE mean?
OBSESSIVE noun- A person who is obsessed, who has an obsession.
- Prone to cause obsession.
- Having one thought or pursuing one activity to the absolute or nearly absolute exclusion of all others.
- Excessive, as results from obsession.