Independent is carrying leader on Rupert Murdoch (4)

I believe the answer is:

iris

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'murdoch' is the definition.
(author Iris Murdoch)

I don't understand how the remainder of the clue works.

(Other definitions for iris that I've seen before include "Female" , "Flag - part of eye" , "Garden flower - part of eye" , "Flag or flower in the eye" , "Ms Murdoch" .)

I've seen this clue in The Sunday Times and The Times.

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