The most common and most likely answer to this crossword clue is the 6 plus 4 letter word ELEVEN PLUS
E
L
E
V
E
N
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.