The most common and most likely answer to this crossword clue is the 13 letter word LICKETY-SPLIT
I've seen this crossword clue in Financial Times
L
I
C
K
E
T
Y
-
S
P
L
I
T
More clues leading to the result LICKETY-SPLIT
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 = lickety-split.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 LICKETY-SPLIT mean?
LICKETY-SPLIT adverb- Quickly; as fast as possible; in short order.