The most common and most likely answer to this crossword clue is the 7 letter word INSIDER
I've seen this crossword clue in The Times
I
N
S
I
D
E
R
More clues leading to the result INSIDER
- Privileged member wearing crimson is on the rise
- Cool leftie is upright person with confidential info
- Privileged member holding office, socialist is backed
- Illegal trader in alcoholic drink spoken of
- Popular team getting runs, one with special advantage
- I think firm must leave someone in privileged position
- Jailed ultimately for this sort of dealing?
- Within radius, one has exclusive knowledge
- Prisoner, maybe, one of an exclusive group
- Possible mole in border, third in garden
Buddy explains!

The straight part
We know that "someone in privileged position" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case someone in privileged position = insider.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 INSIDER mean?
INSIDER noun- A person who has special knowledge about the inner workings of a group, organization, or institution.
- A person who is within an enclosed space.