The most common and most likely answer to this crossword clue is the 7 letter word SHORTLY
I've seen this crossword clue in The Daily Telegraph
S
H
O
R
T
L
Y
Buddy explains!
The straight part
We know that "Before you can say Jack Robinson/in an offhand manner" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case before you can say jack robinson/in an offhand manner = shortly.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 SHORTLY mean?
SHORTLY adverb- In a short or brief time or manner; quickly.
- In or after a short time; soon.
- In few words
- In an irritable ("short") manner.