The most common and most likely answer to this crossword clue is the 8 plus 5 letter word MUSHROOM CLOUD
I've seen this crossword clue in The Guardian
M
U
S
H
R
O
O
M
C
L
O
U
D
Buddy explains!
The straight part
We know that "aftermath of explosion?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case aftermath of explosion? = mushroom cloud.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.