Insignificant contest curtailed in hearing (7)
I believe the answer is:
trivial
'insignificant' is the definition.
('trivial' can be a synonym of 'insignificant')
'contest curtailed in hearing' is the wordplay.
'contest' becomes 'vie' (I've seen this before).
'curtailed' means to remove the last letter.
'in' indicates putting letters inside.
'hearing' becomes 'trial' (I've seen this before).
'vie' with its last letter removed is 'vi'.
'vi' placed inside 'trial' is 'TRIVIAL'.
(Other definitions for trivial that I've seen before include "Unimportant, minor" , "Mundane" , "Slight" , "Meaningless" , "Quite unimportant and paltry" .)