The most common and most likely answer to this crossword clue is the 7 plus 5 letter word CULTURE SHOCK
I've seen this crossword clue in The Times
C
U
L
T
U
R
E
S
H
O
C
K
More clues leading to the result CULTURE SHOCK
Buddy explains!
The straight part
We know that "problem migrants often experience" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case problem migrants often experience = culture shock.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.