The most common and most likely answer to this crossword clue is the 11 letter word ACADEMICIAN
I've seen this crossword clue in The Daily Telegraph
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Buddy explains!

The straight part
We know that "Scholar" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case scholar = academician.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 ACADEMICIAN mean?
ACADEMICIAN noun- A member (especially a senior one) of the faculty at a college or university; an academic.
- A member or follower of an academy, or society for promoting science, art, or literature, such as the French Academy, or the Royal Academy of Arts.