The most common and most likely answer to this crossword clue is the 6 plus 8 letter word COMMON ENTRANCE
I've seen this crossword clue in The Guardian
C
O
M
M
O
N
E
N
T
R
A
N
C
E
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 = common entrance.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.