The most common and most likely answer to this crossword clue is the 11 letter word EXTEMPORISE
I've seen this crossword clue in Independent
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More clues leading to the result EXTEMPORISE
Buddy explains!
The straight part
We know that "Speak without script" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case speak without script = extemporise.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 EXTEMPORISE mean?
EXTEMPORISE verb- To do something, particularly to perform or speak, without prior planning or thought; to act in an impromptu manner; to improvise.
- To do something in a makeshift way.
- To make or create extempore.
- To compose extemporaneously or improvise.