The most common and most likely answer to this crossword clue is the 10 letter word ITINERATED
I've seen this crossword clue in The Guardian
I
T
I
N
E
R
A
T
E
D
Buddy explains!

The straight part
We know that "moved around" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case moved around = itinerated.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 ITINERATED mean?
ITINERATED verb- To travel from place to place, especially to preach or lecture.