This dish, or stick with black olive starter? (5)
I believe the answer is:
gumbo
'this dish' is the definition.
(gumbo is a kind of dish)
'stick with black olive starter?' is the wordplay.
'stick' becomes 'gum' (gum can mean to glue or stick).
'with' is a charade indicator (letters next to each other).
'starter?' indicates taking the first letters (I've seen 'starter' mean this).
The first letters of 'black olive' is 'bo'.
'gum'+'bo'='GUMBO'
'or' acts as a link.
(Other definitions for gumbo that I've seen before include "Spicy soup; okra" , "Spicy Cajun soup" , "Soup from Louisiana" , "Thick soup" , "Okra; spicy Cajun dish" .)