The most common and most likely answer to this crossword clue is the 4 plus 10 letter word NEWS CONFERENCE
I've seen this crossword clue in Financial Times
N
E
W
S
C
O
N
F
E
R
E
N
C
E
More clues leading to the result NEWS CONFERENCE
Buddy explains!

The straight part
We know that "media event" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case media event = news conference.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.