The most common and most likely answer to this crossword clue is the 9 letter word EURIPIDES
I've seen this crossword clue in The Guardian
E
U
R
I
P
I
D
E
S
More clues leading to the result EURIPIDES
- EU with final message on fateful day for famous Greek
- Side ripe for transformation welcoming United's playmaker
- Conveyor of tragedy in English university with final message before fateful day
- Play-maker, current in Peru side, taken out
- Dramatist showing wishful remark from UKIP on fateful day
- Brussels detective travels around
- Foul residue covers irrational tragedian
- Curious pride I harboured in EU’s classical dramatist
- Beaten Peru side includes current play-maker
- Throwing pie is rude old playwright
Buddy explains!
The straight part
We know that "classical dramatist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case classical dramatist = euripides.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.