The most common and most likely answer to this crossword clue is the 13 letter word SCENE-SHIFTER
I've seen this crossword clue in The Times
S
C
E
N
E
-
S
H
I
F
T
E
R
Buddy explains!
The straight part
We know that "This person may appear on stage if the screens need moving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case this person may appear on stage if the screens need moving = scene-shifter.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 SCENE-SHIFTER mean?
SCENE-SHIFTER noun- A stagehand