Hot sauce to accompany Basil and Sybil’s cheese omelettes primarily (7)
I believe the answer is:
tabasco
'hot sauce' is the definition.
(spicy sauce)
'to accompany basil and sybil's cheese omelettes primarily' is the wordplay.
'primarily' suggests taking the first letters.
The first letters of 'to accompany basil and sybils cheese omelettes' is 'TABASCO'.
(Other definitions for tabasco that I've seen before include "condiment?" , "Mexican state; pungent sauce" , "Hot red sauce" , "Hot sauce made from capsicums" , "Spicy pepper sauce" .)