The most common and most likely answer to this crossword clue is the 4 plus 6 letter word HAND PUPPET
I've seen this crossword clue in The Guardian
H
A
N
D
P
U
P
P
E
T
Buddy explains!
The straight part
We know that "a variety act prop" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a variety act prop = hand puppet.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.