The most common and most likely answer to this crossword clue is the 9 letter word RETURNEES
I've seen this crossword clue in Financial Times
R
E
T
U
R
N
E
E
S
More clues leading to the result RETURNEES
Buddy explains!

The straight part
We know that "Re-enter US after moving? They migh" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case re-enter us after moving? they migh = returnees.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 RETURNEES mean?
RETURNEES noun- Someone who comes back or returns, especially to their own country or region.
- A person who sends something back.