Quite insignificant about first of results (6)
I believe the answer is:
pretty
'quite' is the definition.
('pretty' can be a synonym of 'quite')
'insignificant about first of results' is the wordplay.
'insignificant' becomes 'petty' (I've seen this before).
'about' indicates putting letters inside.
'first of' suggests taking the first letters.
The first letter of 'results' is 'r'.
'petty' placed around 'r' is 'PRETTY'.
(Other definitions for pretty that I've seen before include "Moderately" , "Film with Julia Roberts (belle)" , "Fairly - good-looking" , "Pleasing on the eye" , "like a kettle of fish" .)