The most common and most likely answer to this crossword clue is the 6 letter word PRESTO
I've seen this crossword clue in Financial Times
P
R
E
S
T
O
More clues leading to the result PRESTO
- Piano music's silence, with nothing played fast
- At the end stir in sauce very quickly
- Others entering Italian river quickly
- Lancashire football team mostly played very fast
- Heading for Newport having left English city suddenly
- Finger finally entering sauce quickly
- Quickly stop work in Post Office
- River in Italy engulfing remainder very fast
- All others in post office can be very quick
- Balance put in Post Office 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 = presto.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 PRESTO mean?
PRESTO noun- A pair of fives as a starting hand in Texas hold 'em.
- Very fast or quickly; a directive for the musician(s) to play in a very quick tempo.
- Used by magicians when performing a trick; ta-da; voilĂ .