The most common and most likely answer to this crossword clue is the 6 letter word NOMADS
I've seen this crossword clue in The Daily Telegraph
N
O
M
A
D
S
More clues leading to the result NOMADS
- Numbers entertaining deranged tramps?
- Vagrants turned on mother, daughter and son
- Signs agreement enclosing minute area for itinerants
- Itinerants’ son heads west eating bananas
- Numbers must be inclusive of irate people always on the move
- Homeless types with boy going round collecting nuts
- Definitely not nuts, initially supporting Wanderers
- Boy knocked over when interrupted by idiotic folk on the move
- Seasonal travellers are so damn stupid
- Boy raised to gather nuts for travellers
Buddy explains!

The straight part
We know that "people always on the move" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case people always on the move = nomads.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 NOMADS mean?
NOMADS noun- A member of a society or class who herd animals from pasture to pasture with no fixed home.
- A person who changes residence frequently.
- A player who changes teams frequently.
- One who wanders, who travels aimlessly.
- Any of various far-migrating nymphalid butterflies of the genus Danaus.
- The wandering albatross, Diomedea exulans.