The most common and most likely answer to this crossword clue is the 9 letter word NOVELETTE
I've seen this crossword clue in The Guardian
N
O
V
E
L
E
T
T
E
More clues leading to the result NOVELETTE
- Story of new love upset by contents of letter
- Little work requiring 15 days and lots of character?
- Written work takes half a month and then correspondence is incomplete
- Note exposed billet-doux as work of fiction
- Bill’s written about short dance in work of fiction
- English character cut after month in story
- A long short story that's fresh, but gets dry after 6th chapter and routine at the end
- Little story with new and better content
Buddy explains!

The straight part
We know that "Written work" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case written work = novelette.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.
What does NOVELETTE mean?
NOVELETTE noun- A short novel.
- A short piece of lyrical music, especially one for the piano.