Be a chauvinist, dismissing leader (5)

I believe the answer is:

exist

'be' is the definition.
('exist' can be a synonym of 'be')

'a chauvinist dismissing leader' is the wordplay.
'a chauvinist' becomes 'sexist'.
'dismissing leader' means to remove the first letter.
'sexist' with its first letter taken away is 'EXIST'.

(Other definitions for exist that I've seen before include "Scrape by" , "Live" , "Have objective reality" , "Have being or continue living" , "Survive" .)

I've seen this clue in The Times.

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