The most common and most likely answer to this crossword clue is the 3 plus 3 plus 7 letter word PAY AND DISPLAY
I've seen this crossword clue in The Daily Telegraph
P
A
Y
A
N
D
D
I
S
P
L
A
Y
More clues leading to the result PAY AND DISPLAY
Buddy explains!

The straight part
We know that "parking scheme" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parking scheme = pay and display.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 PAY AND DISPLAY mean?
PAY AND DISPLAY adjective- Describing a car park in which the motorist obtains a ticket (for a specified period) from a coin-operated machine and displays it in the car so it can be checked by a parking attendant.