The most common and most likely answer to this crossword clue is the 14 letter word INTELLIGENTSIA
I've seen this crossword clue in The Daily Telegraph
I
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T
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I
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A
More clues leading to the result INTELLIGENTSIA
- “Elitist leaning” may represent us
- Bright bunch working for TV hearing news as it breaks
- Cognoscenti confused senile litigant
- Complicated lines gain title for eggheads
- Guys having cultivated learning – elitist? Not right!
- Eggheads showing foolish elitist leaning
- International tangle? Listen, I straightened out this clever set
- Elitist-leaning set?
- People really smart and elegant in list I revised
- Eggheads with terribly elitist leaning
Buddy explains!

The straight part
We know that "Eggheads" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eggheads = intelligentsia.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 INTELLIGENTSIA mean?
INTELLIGENTSIA noun- The intellectual élite of a society (especially in nineteenth-century Poland, in Russia and later the Soviet Union).