The most common and most likely answer to this crossword clue is the 4 letter word WINK
I've seen this crossword clue in The Daily Telegraph
W
I
N
K
Buddy explains!

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 WINK mean?
WINK noun- An act of winking (a blinking of only one eye), or a message sent by winking.
- A brief period of sleep; especially forty winks.
- A brief time; an instant.
- The smallest possible amount.
- A subtle allusion.
- To close one's eyes in sleep.
- To close one's eyes.
- Usually followed by at: to look the other way, to turn a blind eye.
- To close one's eyes quickly and involuntarily; to blink.
- To blink with only one eye as a message, signal, or suggestion, usually with an implication of conspiracy. (When transitive, the object may be the eye being winked, or the message being conveyed.)
- To gleam fitfully or intermitently; to twinkle; to flicker.
- A disc used in the game of tiddlywinks.
- (Chiefly British) Periwinkle.