The most common and most likely answer to this crossword clue is the 7 letter word GRAVITY
I've seen this crossword clue in The Daily Telegraph
G
R
A
V
I
T
Y
More clues leading to the result GRAVITY
- Seriousness of natural attraction
- Force uses ill-gotten gains to control Congress
- Seriousness will tend to keep you grounded
- Sauce holding Italian’s earthy attraction
- Possible reason for dropping it in juice
- What’s responsible for sinking? Something in boat’s broken by it
- Sex appeal in stock attractive influence
- It’s lacking in seriousness producing extra money
- Extreme importance of the thing put into meaty juice
- It’s covered in sauce — that’ll bring you down to earth
Buddy explains!

The straight part
We know that "Extreme importance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extreme importance = gravity.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 GRAVITY mean?
GRAVITY noun- The state or condition of having weight; weight; heaviness.
- The state or condition of being grave; seriousness.
- The lowness of a note.
- Force on Earth's surface, of the attraction by the Earth's masses, and the centrifugal pseudo-force caused by the Earth's rotation, resulting from gravitation.
- (in casual discussion, also) Gravitation, universal force exercised by two bodies onto each other (gravity and gravitation are often used interchangeably).
- Specific gravity.