Ad-libbing station jingle is foolish (11)

I believe the answer is:

improvident

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'foolish' is the definition.
Both the definition and answer are adjectives. Perhaps they are linked in a way I don't understand?

I don't understand the remainder of the clue.

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(Other definitions for improvident that I've seen before include "Lacking foresight - spendthrift" , "Careless" , "Thoughtless" , "unprepared for what's to come?" , "Not thrifty" .)

I've seen this clue in The Times.

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