The most common and most likely answer to this crossword clue is the 6 letter word GREATS
I've seen this crossword clue in The Daily Telegraph
G
R
E
A
T
S
More clues leading to the result GREATS
Buddy explains!
The straight part
We know that "important people" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case important people = greats.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 GREATS mean?
GREATS noun- A person of major significance, accomplishment or acclaim.
- The main division in a pipe organ, usually the loudest division.
- (in combinations such as "two-greats", "three-greats" etc.) An instance of the word "great" signifying an additional generation in phrases expressing family relationships.