The most common and most likely answer to this crossword clue is the 7 plus 7 letter word DRIVING LICENCE
I've seen this crossword clue in The Daily Telegraph
D
R
I
V
I
N
G
L
I
C
E
N
C
E
Buddy explains!
The straight part
We know that "Motorists may show this" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case motorists may show this = driving licence.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.