The most common and most likely answer to this crossword clue is the 9 letter word SOPHOCLES
I've seen this crossword clue in The Daily Telegraph
S
O
P
H
O
C
L
E
S
More clues leading to the result SOPHOCLES
- Mixed school's PE displays a Greek character
- Having shot hoops, see the French playmaker
- Almost closed shop arranged for one who worked in theatre
- Dramatist‘s second work — this classical reading son ignored
- Greek dramatist breaks to pocket first of cash, after bribe
- Ancient Greek hotel cesspool erupted
- Serious writer‘s concession: a little comedy in the gaps
- Dramatist playing polo and chess
- Playwright’s shop close to collapse
- Dramatist chooses LP in new compilation
Buddy explains!

The straight part
We know that "Dramatist" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dramatist = sophocles.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.