The most common and most likely answer to this crossword clue is the 13 letter word HEARTBREAKERS
I've seen this crossword clue in The Times
H
E
A
R
T
B
R
E
A
K
E
R
S
Buddy explains!
The straight part
We know that "they cause grief" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they cause grief = heartbreakers.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 HEARTBREAKERS mean?
HEARTBREAKERS noun- Someone, usually attractive, who flirts with or otherwise enamours a person, but does not reciprocate their love.
- Something that causes sorrow, grief or extreme disappointment.
- A match which ends in defeat for a promising player or team.
- An independent role-playing game that attempts to fix various perceived design flaws in an established RPG, but whose few innovations will not reach a wide audience due to its lack of marketability.
- A curl or lovelock.