Improvise detailed explanation of whereabouts to protect daughter (2-3)

I believe the answer is:

ad-lib

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'improvise' is the definition.
(I know that improvise can be written as ad-lib)

I cannot understand how the remainder of the clue works.

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(Other definitions for ad-lib that I've seen before include "without restraint" , "Speak off the cuff" , "Extemporise" , "freely" , "Speak without preparation" .)

I've seen this clue in The Independent.

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