The most common and most likely answer to this crossword clue is the 9 letter word AESCHYLUS
I've seen this crossword clue in The Times
A
E
S
C
H
Y
L
U
S
More clues leading to the result AESCHYLUS
- Hard to crack clues say rewritten for tragic author
- Such easy puzzles, containing hint of Latin and ancient Greek
- Clue “shy” as anagram
- Classical writer’s character that’s old, extremely hearty and mostly drunk
- Playwright imaginatively uses alchemy — but no space for printing here
- Dramatist creating hussy done up with lace
Buddy explains!

The straight part
We know that "tragic author" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tragic author = aeschylus.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.