Chauvinist doesn’t start to live (5)
I believe the answer is:
exist
'live' is the definition.
(I know that live can be written as exist)
'chauvinist doesn't start' is the wordplay.
'chauvinist' becomes 'sexist' (I've seen this in another clue).
'doesn't start' means to remove the first letter.
'sexist' with its initial letter taken away is 'EXIST'.
'to' acts as a link.
(Other definitions for exist that I've seen before include "Have being or continue living" , "Survive" , "Live" , "Scrape by" , "Be alive" .)