Cryptic crossword clue
Done with PM’s backing — Sun perhaps fails to respond to alarm 10

The most common and most likely answer to this crossword clue is the 10 letter word OVERSLEEPS

I've seen this crossword clue in The Guardian
O
V
E
R
S
L
E
E
P
S

Buddy explains!

The straight part
We know that "perhaps fails to respond to alarm" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case perhaps fails to respond to alarm = oversleeps.
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 OVERSLEEPS mean?

OVERSLEEPS verb
  1. To sleep for longer than intended.
  2. To sleep for longer than one intended.
  3. To sleep beyond (a given time), to sleep through (an event etc.).

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