That lady's selfless successor (3)

I believe the answer is:

her

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'that lady's' is the definition.
('her' refers to a woman)

I can't explain the rest of the clue.

(Other definitions for her that I've seen before include "She, objectively" , "The woman's" , "The female's" , "That lady's" , "Pronoun used of ship" .)

I've seen this clue in The Independent.

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