The most common and most likely answer to this crossword clue is the 9 letter word EGOTISTIC
I've seen this crossword clue in The Guardian
E
G
O
T
I
S
T
I
C
More clues leading to the result EGOTISTIC
- Self-centred, I get Stoic for a change
- Rubbish old git cites is all about me?
- Self-centred stoic, eg perversely holds it back
- Self-important drunk goes round knocking back vermouth accompanied by jerk
- Self-centred European obtained first integrated circuit
- Superior cities got refurbished
- Got into chaotic cities in vain
Buddy explains!
The straight part
We know that "Self-centred" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case self-centred = egotistic.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.