The most common and most likely answer to this crossword clue is the 8 plus 8 letter word ORDERÂ OF THEÂ BOOT
I've seen this crossword clue in The Guardian
O
R
D
E
R
Â
O
F
T
H
E
Â
B
O
O
T
Buddy explains!
The straight part
We know that "Dismissal" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dismissal = order of the boot.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.