The most common and most likely answer to this crossword clue is the 3 plus 4 plus 3 plus 5 letter word RUN DOWN THE CLOCK
I've seen this crossword clue in The Guardian
R
U
N
D
O
W
N
T
H
E
C
L
O
C
K
More clues leading to the result RUN DOWN THE CLOCK
Buddy explains!
The straight part
We know that "hold on, hoping for the best" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case hold on, hoping for the best = run down the clock.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.