The most common and most likely answer to this crossword clue is the 8 letter word SHORTCUT
I've seen this crossword clue in The Times
S
H
O
R
T
C
U
T
More clues leading to the result SHORTCUT
Buddy explains!

The straight part
We know that "Quick way round" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case quick way round = shortcut.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 SHORTCUT mean?
SHORTCUT noun- A path between two points that is faster than the commonly used paths.
- A method to accomplish something that omits one or more steps.
- (in the Microsoft family of operating systems) A file that points to the location of another file and serves as a quick way to access it.
- A keyboard shortcut: a combination of keystrokes that provides easier access to a command or operation.
- To take or use a shortcut