The most common and most likely answer to this crossword clue is the 4 letter word SOUK
I've seen this crossword clue in The Guardian
S
O
U
K
More clues leading to the result SOUK
Buddy explains!

The straight part
We know that "open-air market" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case open-air market = souk.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 SOUK mean?
SOUK noun- A street market, particularly in Arabic- and Somali-speaking countries; a place where people buy and sell goods.