The most common and most likely answer to this crossword clue is the 4 plus 3 letter word SKID LID
I've seen this crossword clue in The Times
S
K
I
D
L
I
D
More clues leading to the result SKID LID
Buddy explains!
The straight part
We know that "safer with this on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case safer with this on = skid lid.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.