Case finishing early, having involved one with very minor matters (6)
I believe the answer is:
trivia
'minor matters' is the definition.
(I've seen this in another clue)
'case finishing early having involved one with' is the wordplay.
'case' becomes 'trial' (court case).
'finishing early' means to remove the last letter (the word finishes earlier than normal).
'having' is an insertion indicator.
'involved one with' becomes 'iv' (I am not sure about this - if you are sure you should believe this answer much more).
'trial' with its last letter removed is 'tria'.
'tria' placed around 'iv' is 'TRIVIA'.
'very' acts as a link.
Can you help me to learn more?
(Other definitions for trivia that I've seen before include "The details of little or no importance" , "Matters very little" , "Things of little importance" , "Trifles, unimportant details" , "Unimportant things, don't waste time on them" .)