The most common and most likely answer to this crossword clue is the 5 plus 4 letter word MOTOR HOME
M
O
T
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H
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M
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Buddy explains!
The straight part
We know that "moving house" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moving house = motor home.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 MOTOR HOME mean?
MOTOR HOME noun- A type of recreational vehicle, a self-propelled structure built on a truck or bus chassis containing living accommodations.