The most common and most likely answer to this crossword clue is the 6 letter word MATTER
I've seen this crossword clue in The Times
M
A
T
T
E
R
More clues leading to the result MATTER
- Queen looked down upon by dull subject
- Affair to be of consequence
- Prosaic concern, not on law
- See 16ac.
- Count carrying more weight after transitioning
- Mother drinking Tango becomes issue
- Topic – dull, I hesitate to say
- Concern parent’s shown about infant, finally
- Stuff what’s up?
- Commonplace affair, rotten deed
Buddy explains!

The straight part
We know that "of consequence" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of consequence = matter.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 MATTER mean?
MATTER noun- Substance, material.
- A condition, subject or affair, especially one of concern.
- An approximate amount or extent.
- The essence; the pith; the embodiment.
- Inducing cause or reason, especially of anything disagreeable or distressing.
- Pus.
- To be important.
- (in negative constructions) To care about, to mind; to find important.
- To form pus or matter, as an abscess; to maturate.