Back smart type of fellow to embrace independent woman (5)

I believe the answer is:

celia

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'woman' is the definition.

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

(Other definitions for celia that I've seen before include "Frederick's daughter" , "Daughter to Frederick" , "lady" , "Character in Tales from Shakespeare" , "Rosalind's cousin" .)

I've seen this clue in The Guardian.

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