The most common and most likely answer to this crossword clue is the 9 letter word POSTHASTE
I've seen this crossword clue in The Times
P
O
S
T
H
A
S
T
E
More clues leading to the result POSTHASTE
- Pa gets drunk with shots, having drained three at once
- Quickly running past those
- Posse that disperses at a gallop
- Quickly giving compere stick if introductions mixed up
- Express as 20, perhaps?
- First-class mail should have this now!
- Those taps turned quickly
- Model that’s changed inside very quickly
- Quickly pass to the suspect
- Quickly adopt an attitude that’s flexible, to be accepted
Buddy explains!

The straight part
We know that "at once" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case at once = posthaste.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 POSTHASTE mean?
POSTHASTE noun- A great hurry.
- Quickly, as fast as someone travelling post; with great speed