The most common and most likely answer to this crossword clue is the 4 plus 11 letter word ORAL EXAMINATION
I've seen this crossword clue in The Sunday Telegraph
O
R
A
L
E
X
A
M
I
N
A
T
I
O
N
More clues leading to the result ORAL EXAMINATION
Buddy explains!
The straight part
We know that "Testing event for student" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case testing event for student = oral examination.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.