The most common and most likely answer to this crossword clue is the 9 letter word PARANOIAC
I've seen this crossword clue in The Times
P
A
R
A
N
O
I
A
C
Buddy explains!
The straight part
We know that "delusional" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case delusional = paranoiac.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 PARANOIAC mean?
PARANOIAC noun- Somebody who has paranoia, a paranoid person.
- Pertaining to, or exhibiting, paranoia.