The most common and most likely answer to this crossword clue is the 9 letter word EXTEMPORE
I've seen this crossword clue in The Guardian
E
X
T
E
M
P
O
R
E
More clues leading to the result EXTEMPORE
- Unprepared before accepting Times rate
- Irregular worker finding gold in river unplanned
- Unscripted show in which police upset over engineers
- Old lover wants casual alternative, essentially sex that’s spontaneous
- Unguardedly messages one back, opening spontaneously
- Without preparation, extreme confusion surrounds Post Office
- Old-time engineers like making it up as they go along
- Poet inflamed with mere kiss that’s spontaneous
- Leader of Opposition in bad temper after European vote, but with no plan
- Off the cuff, so to speak
Buddy explains!

The straight part
We know that "Off the cuff, so to speak" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case off the cuff, so to speak = extempore.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 EXTEMPORE mean?
EXTEMPORE noun- Something improvised.
- Carried out with no preparation; impromptu.
- Without preparation; extemporaneously.