The most common and most likely answer to this crossword clue is the 8 letter word LONGHAND
I've seen this crossword clue in The Daily Telegraph
L
O
N
G
H
A
N
D
Buddy explains!

The straight part
We know that "Writing" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case writing = longhand.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 LONGHAND mean?
LONGHAND noun- The written characters used in the common method of writing; opposed to shorthand, or typing or printing; handwriting.
- Written by hand in normal characters, as opposed to shorthand.
- Written by hand (with pen or pencil), rather than printed out; handwritten.