The most common and most likely answer to this crossword clue is the 10 letter word WHIP-ROUND
I've seen this crossword clue in The Guardian
W
H
I
P
-
R
O
U
N
D
Buddy explains!
The straight part
We know that "Way to get a kitty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case way to get a kitty = whip-round.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 WHIP-ROUND mean?
WHIP-ROUND noun- A quick collection of money from a group of people, usually for a beneficial purpose.