The most common and most likely answer to this crossword clue is the 11 letter word ELEVEN-PLUS
I've seen this crossword clue in The Guardian
E
L
E
V
E
N
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P
L
U
S
Buddy explains!
The straight part
We know that "Exam" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case exam = eleven-plus.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 ELEVEN-PLUS mean?
ELEVEN-PLUS noun- An examination formerly administered to all students in their final year of primary education, now used only in a few counties of England and Northern Ireland.