The most common and most likely answer to this crossword clue is the 4 plus 5 plus 5 letter word FULL STEAM AHEAD
I've seen this crossword clue in The Guardian
F
U
L
L
S
T
E
A
M
A
H
E
A
D
Buddy explains!
The straight part
We know that "get forward quickly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case get forward quickly = full steam ahead.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.