Crossword Genius

Be unfair to her, maybe, starting a little late (5)

Ross

I believe the answer is:

exist

'be' is the definition.
(synonyms)

'unfair to her maybe starting a little late' is the wordplay.
I cannot quite understand how this works, but
'late' could be 'ex' (prefix meaning former or onetime) and 'ex' is found within the answer.
The remaining letters 'ist' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

(Other definitions for exist that I've seen before include "Subsist" , "Have being or continue living" , "Get a life!" , "quick!" , "Live" .)

I've seen this clue in The Times.
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