The most common and most likely answer to this crossword clue is the 6 letter word PROMPT
I've seen this crossword clue in The Daily Telegraph
P
R
O
M
P
T
More clues leading to the result PROMPT
Buddy explains!

The straight part
We know that "Quick" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quick = prompt.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 PROMPT mean?
PROMPT noun- A reminder or cue.
- A time limit given for payment of an account for produce purchased, this limit varying with different goods.
- A sequence of characters that appears on a monitor to indicate that the computer is ready to receive input.
- (writing) A suggestion for inspiration given to an author.
- To lead (someone) toward what they should say or do.
- To show or tell an actor/person the words they should be saying, or actions they should be doing.
- To initiate; to cause or lead to.
- Quick; acting without delay.
- On time; punctual.
- Ready; willing to act.