The most common and most likely answer to this crossword clue is the 6 letter word PRONTO
I've seen this crossword clue in Financial Times
P
R
O
N
T
O
More clues leading to the result PRONTO
- In favour of not running quickly
- Immediately aware of following publicity experts
- Public Record Office not working quickly
- Drunk on port? At once!
- Immediately in favour of not getting pissed
- Quickly suspicious of giving support to voting system
- Pair aware of prompt
- In favour of hiding old books at once
- Expert locks up old books without delay
- Communications officer starts to name the others immediately
Buddy explains!

The straight part
We know that "Quickly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quickly = pronto.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 PRONTO mean?
PRONTO adverb- Quickly, very soon, promptly.