The most common and most likely answer to this crossword clue is the 7 letter word AIRSIDE
I've seen this crossword clue in Financial Times
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More clues leading to the result AIRSIDE
Buddy explains!

The straight part
We know that "Where past customs are on the way out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where past customs are on the way out = airside.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 AIRSIDE mean?
AIRSIDE adjective- In a passenger-only area of an airport (beyond passport and customs control)
- Into the passenger-only area of an airport (beyond passport and customs control)