Flung niece out with no good effect (9)

I believe the answer is:

influence

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'effect' is the definition.
(I know that influence is a type of effect)

I can't explain the rest of the clue.

(Other definitions for influence that I've seen before include "Sway, dominance" , "Clue in fen (anag.)" , "Power to affect persons or events" , "The capacity to affect others" , "Weight" .)

I've seen this clue in The Telegraph.

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