The most common and most likely answer to this crossword clue is the 5 plus 8 letter word ZEBRA CROSSING
I've seen this crossword clue in The Times
Z
E
B
R
A
C
R
O
S
S
I
N
G
Buddy explains!
The straight part
We know that "Pedestrians have priority here – it’s black and white!" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case pedestrians have priority here – it’s black and white! = zebra crossing.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.