The most common and most likely answer to this crossword clue is the 5 plus 3 plus 10 letter word SKULL AND CROSSBONES
I've seen this crossword clue in The Times
S
K
U
L
L
A
N
D
C
R
O
S
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B
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N
E
S
More clues leading to the result SKULL AND CROSSBONES
Buddy explains!
The straight part
We know that "Deathly reminder" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deathly reminder = skull and crossbones.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.