The most common and most likely answer to this crossword clue is the 3 plus 6 plus 5 letter word GUY FAWKES NIGHT
I've seen this crossword clue in The Daily Telegraph
G
U
Y
F
A
W
K
E
S
N
I
G
H
T
Buddy explains!
The straight part
We know that "Regular event, seeing a rebellious chap get fired" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case regular event, seeing a rebellious chap get fired = guy fawkes night.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.