The most common and most likely answer to this crossword clue is the 10 letter word PIRANDELLO
I've seen this crossword clue in The Times
P
I
R
A
N
D
E
L
L
O
More clues leading to the result PIRANDELLO
- Dramatist quietly crossing river, and later wooded hollow
- Quiet look around Ireland moved Sicilian dramatist
- River engulfing valley after current flowed
- Post office in country valley – just the opposite!
- Italian writer polled unexpectedly about part of Middle East
- Dramatist’s country valley edged by Italian river
- Playwright in group: “I ran Dell operations”
- Playwright’s country valley circled by Italian river
- Author from Sicily and I fled valley, falling into Italian river
Buddy explains!

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