Short test covering four inconsequential facts (6)
I believe the answer is:
trivia
'inconsequential facts' is the definition.
(I've seen this before)
'short test covering four' is the wordplay.
'short' means to remove the last letter.
'test' becomes 'tax'.
'covering' means one lot of letters goes inside another.
'four' becomes 'rivi' (I am not sure about this - if you are sure you should believe this answer much more).
'tax' with its last letter taken away is 'ta'.
'ta' enclosing 'rivi' is 'TRIVIA'.
(Other definitions for trivia that I've seen before include "minor points of interest?" , "petty considerations" , "Minor details" , "Unimportant things, don't waste time on them" , "Unimportant or valueless things" .)