The most common and most likely answer to this crossword clue is the 10 letter word TRAMONTANE
I've seen this crossword clue in Independent
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Buddy explains!

The straight part
We know that "Perhaps crossing Alps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case perhaps crossing alps = tramontane.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 TRAMONTANE mean?
TRAMONTANE noun- A dry, cold north wind in Italy and adjacent Mediterranean areas.
- One living beyond the mountains; a foreigner; a stranger.
- From the far side of the mountains (especially from North of the Alps)
- Foreign
- A classical name for the north wind