Business that's pretty good after a false start (6)
I believe the answer is:
affair
'business' is the definition.
(I've seen this in another clue)
'pretty good after a false start' is the wordplay.
'pretty good' becomes 'fair' (both can mean of sufficient quality).
'after' is a charade indicator (letters next to each other).
'start' says to take the initial letters.
The initial letter of 'false' is 'f'.
'a'+'f'='af'
'fair' after 'af' is 'AFFAIR'.
'that's' acts as a link.
(Other definitions for affair that I've seen before include "A romantic intrigue" , "A matter, perhaps of love" , "connected with love" , "Raffia (anag)" , "Business; romance" .)