The most common and most likely answer to this crossword clue is the 13 letter word HOUSE-HUNTING
I've seen this crossword clue in The Guardian
H
O
U
S
E
-
H
U
N
T
I
N
G
Buddy explains!

The straight part
We know that "Wanting to move/Wanting to move" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wanting to move/wanting to move = house-hunting.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 HOUSE-HUNTING mean?
HOUSE-HUNTING noun- The search for a suitable house to buy or rent.