The most common and most likely answer to this crossword clue is the 8 letter word PLAY-ACT
I've seen this crossword clue in The Guardian
P
L
A
Y
-
A
C
T
More clues leading to the result PLAY-ACT
Buddy explains!

The straight part
We know that "Make believe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make believe = play-act.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 PLAY-ACT mean?
PLAY-ACT verb- To play a role.