The most common and most likely answer to this crossword clue is the 7 letter word PLAYERS
I've seen this crossword clue in The Guardian
P
L
A
Y
E
R
S
More clues leading to the result PLAYERS
Buddy explains!

The straight part
We know that "People who pretend/to be influential" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case people who pretend/to be influential = players.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 PLAYERS mean?
PLAYERS noun- One that plays
- One who is playful; one without serious aims; an idler; a trifler.
- A significant participant.
- A person who plays the field rather than having a long-term sexual relationship.