The most common and most likely answer to this crossword clue is the 7 letter word TRIVIAL
I've seen this crossword clue in Independent
T
R
I
V
I
A
L
More clues leading to the result TRIVIAL
- Pilot admitting sex is meaningless
- Petty criminal may be up for it - sex in custody
- Enter four or six in test? Of little importance
- Minor hearing about sex in Rome
- Mickey Mouse I have briefly put in trouble
- Hearing about four or six piddling
- Six in court case that’s unimportant
- Case full of French wine mostly, but no great shakes
- Inconsequential number involved in action
- Sextet entering competition that’s inconsequential
Buddy explains!

The straight part
We know that "Of little importance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of little importance = trivial.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TRIVIAL mean?
TRIVIAL noun- Any of the three liberal arts forming the trivium.
- Ignorable; of little significance or value.
- Commonplace, ordinary.
- Concerned with or involving trivia.
- Relating to or designating the name of a species; specific as opposed to generic.
- Of, relating to, or being the simplest possible case.
- Self-evident.
- Pertaining to the trivium.
- Indistinguishable in case of truth or falsity.