The most common and most likely answer to this crossword clue is the 7 plus 4 letter word VARIETY SHOW
I've seen this crossword clue in The Sunday Telegraph
V
A
R
I
E
T
Y
S
H
O
W
Buddy explains!
The straight part
We know that "Performance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case performance = variety show.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.