The most common and most likely answer to this crossword clue is the 11 plus 4 letter word BESTÂ BEFORE DATE
I've seen this crossword clue in The Guardian
B
E
S
T
Â
B
E
F
O
R
E
D
A
T
E
Buddy explains!
The straight part
We know that "Things aren’t so good after that" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case things aren’t so good after that = best before date.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.