The most common and most likely answer to this crossword clue is the 8 letter word ROADSHOW
I've seen this crossword clue in The Daily Telegraph
R
O
A
D
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H
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W
More clues leading to the result ROADSHOW
Buddy explains!
The straight part
We know that "A moving sort of entertainment" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a moving sort of entertainment = roadshow.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 ROADSHOW mean?
ROADSHOW noun- A show that travels from place to place.
- To show in various places as part of a travelling excursion.