The most common and most likely answer to this crossword clue is the 9 letter word EGOMANIAC
I've seen this crossword clue in The Guardian
E
G
O
M
A
N
I
A
C
More clues leading to the result EGOMANIAC
- Try to stop dissipation of anaemic narcissist
- Number one fan?
- Try to lance anaemic wound, being totally self-obsessed
- Passionate believer in everything about him
- For example, ordinary daffy. Narcissus was one
- Narcissist, say, old bloke in charge across America
- I manage leading pair of companies badly, but I can’t imagine anyone else in the job!
- What a bighead! Come again? Rephrase that!
- Character primarily on a mega 'I' trip?
- Arrogant individual's come again, unfortunately
Buddy explains!
The straight part
We know that "being totally self-obsessed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case being totally self-obsessed = egomaniac.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 EGOMANIAC mean?
EGOMANIAC noun- A person obsessed with their own (supposed) importance.