The most common and most likely answer to this crossword clue is the 7 plus 3 plus 5 letter word WEATHER THE STORM
I've seen this crossword clue in The Daily Telegraph
W
E
A
T
H
E
R
T
H
E
S
T
O
R
M
Buddy explains!
The straight part
We know that "pull through" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pull through = weather the storm.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.