The most common and most likely answer to this crossword clue is the 5 plus 2 plus 3 plus 4 letter word SAVED BY THE BELL
I've seen this crossword clue in The Guardian
S
A
V
E
D
B
Y
T
H
E
B
E
L
L
Buddy explains!
The straight part
We know that "given a last-minute reprieve" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case given a last-minute reprieve = saved by the bell.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.