Crossword Genius

Bitterness of wife fired from golf club (4)

Ross

I believe the answer is:

edge

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'bitterness' is the definition.
(thesaurus)

I cannot understand how the remainder of the clue works.

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(Other definitions for edge that I've seen before include "incisiveness" , "Inch; border" , "Move little by little to the border" , "Guitarist with U2" , "Snick - boundary" .)

I've seen this clue in The Telegraph.
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