The most common and most likely answer to this crossword clue is the 3 plus 4 letter word BIG SHOT
I've seen this crossword clue in The Times
B
I
G
S
H
O
T
More clues leading to the result BIG SHOT
- Somebody's mum pinched by sexist?
- One who’s directing sexist perhaps to keep quiet
- Notable racist welcoming leaders in spiky helmets
- Somebody racist, perhaps, should keep quiet
- Top table type maybe with GSOH clowning in short while
- Influential person’s large ball
- VIP hater keeping quiet
- Somebody racist keeps quiet!
- Heavyweight cannonball?
Buddy explains!

The straight part
We know that "Somebody" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case somebody = big shot.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.