Having read abridged bible, sadly one strays from the text (2-6)

I believe the answer is:

ad-libber

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'one strays from the text' is the definition.
(actor who improvises new lines)

'having read abridged bible sadly' is the wordplay.
I cannot really understand how this works, but
an anagram of 'bible' is 'libbe' which is present in the answer.
This explanation may well be incorrect...

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I've seen this clue in The Guardian.

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