The most common and most likely answer to this crossword clue is the 4 letter word EGOS
I've seen this crossword clue in The Times
E
G
O
S
More clues leading to the result EGOS
- Heads of European governments with outsize conceits
- Is Best essentially keeping fit?
- More than once, I say so contrarily
- For example, very large feelings of superiority
- Opponents securing game — might they become inflated?
- They can become inflated, say, and very large
- They’re crushed if clue goes unsolved
- They may be inflated, say, and very large
- For example, very big personalities
- Goes wild for big heads
Buddy explains!

The straight part
We know that "conceits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case conceits = egos.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 EGOS mean?
EGOS noun- The self, especially with a sense of self-importance.
- (Freudian) The most central part of the mind, which mediates with one's surroundings.