The most common and most likely answer to this crossword clue is the 4 letter word PEEP
I've seen this crossword clue in The Daily Telegraph
P
E
E
P
Buddy explains!
The straight part
We know that "Have quick look in either direction" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case have quick look in either direction = peep.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 PEEP mean?
PEEP noun- A quiet sound, particularly one from a baby bird.
- A feeble utterance or complaint.
- The sound of a steam engine's whistle; typically shrill.
- A kind of bird; a sandpiper.
- To make a soft, shrill noise like a baby bird.
- To speak briefly with a quiet voice.
- A quick look or glimpse, especially a furtive one.
- The first partial appearance of something; a beginning to appear.
- To look, especially through a narrow opening, or while trying not to be seen or noticed.
- To begin to appear; to look forth from concealment; to make the first appearance.
- A spot on a die or domino.
- Person.