The most common and most likely answer to this crossword clue is the 5 letter word SWIFT
I've seen this crossword clue in The Daily Telegraph
S
W
I
F
T
Buddy explains!

The straight part
We know that "Quick/writer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quick/writer = swift.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 SWIFT mean?
SWIFT noun- A small plain-colored bird of the family Apodidae that resembles a swallow and is noted for its rapid flight.
- Any of certain lizards of the genus Sceloporus.
- A moth of the family Hepialidae, swift moth, ghost moth.
- Any of various fast-flying hesperiid butterflies.
- A reel for winding yarn.
- The main cylinder of a carding-machine.
- The current of a stream.
- Fast; quick; rapid.
- Capable of moving at high speeds.
- Swiftly.