The most common and most likely answer to this crossword clue is the 11 letter word PARENTHESES
I've seen this crossword clue in The Sunday Telegraph
P
A
R
E
N
T
H
E
S
E
S
Buddy explains!
The straight part
We know that "afterthoughts/afterthoughts" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case afterthoughts/afterthoughts = parentheses.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.
What does PARENTHESES mean?
PARENTHESES noun- A clause, phrase or word which is inserted (usually for explanation or amplification) into a passage which is already grammatically complete, and usually marked off with brackets, commas or dashes.
- Either of a pair of brackets, especially round brackets, ( and ) (used to enclose parenthetical material in a text).
- A digression; the use of such digressions.
- Such brackets as used to clarify expressions by grouping those terms affected by a common operator, or to enclose the components of a vector or the elements of a matrix.