The most common and most likely answer to this crossword clue is the 5 letter word CLOSE
I've seen this crossword clue in The Times
C
L
O
S
E
More clues leading to the result CLOSE
Buddy explains!

The straight part
We know that "Big shots" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case big shots = close.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 CLOSE mean?
CLOSE noun- An end or conclusion.
- The manner of shutting; the union of parts; junction.
- A grapple in wrestling.
- The conclusion of a strain of music; cadence.
- A double bar marking the end.
- (travel) The time when checkin staff will no longer accept passengers for a flight.
- (physical) To remove a gap.
- (social) To finish, to terminate.
- To come or gather around; to enclose; to encompass; to confine.
- To have a vector sum of 0; that is, to form a closed polygon.
- (chiefly Yorkshire) An enclosed field.
- (chiefly British) A street that ends in a dead end.
- A very narrow alley between two buildings, often overhung by one of the buildings above the ground floor.
- The common staircase in a tenement.
- A cathedral close.
- The interest which one may have in a piece of ground, even though it is not enclosed.
- Closed, shut.
- Narrow; confined.
- At a little distance; near.
- Intimate; well-loved.
- Oppressive; without motion or ventilation; causing a feeling of lassitude.
- (Ireland, England, Scotland) Hot, humid, with no wind.
- (of a vowel) Articulated with the tongue body relatively close to the hard palate.
- Strictly confined; carefully guarded.
- Out of the way of observation; secluded; secret; hidden.
- Nearly equal; almost evenly balanced.
- Short.
- Dense; solid; compact.
- Concise; to the point.
- Difficult to obtain.
- Parsimonious; stingy.
- Adhering strictly to a standard or original; exact.
- Accurate; careful; precise; also, attentive; undeviating; strict.
- Marked, evident.