The most common and most likely answer to this crossword clue is the 4 plus 3 plus 6 letter word BELT AND BRACES
B
E
L
T
A
N
D
B
R
A
C
E
S
More clues leading to the result BELT AND BRACES
Buddy explains!
The straight part
We know that "double security" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case double security = belt and braces.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.