Vehicles carrying, say, those on a diet (6)
I believe the answer is:
vegans
'those on a diet' is the definition.
(people with a specific diet)
'vehicles carrying say' is the wordplay.
'vehicles' becomes 'vans' (van is a kind of vehicle).
'carrying' is an insertion indicator.
'say' becomes 'eg'.
'vans' placed around 'eg' is 'VEGANS'.
(Other definitions for vegans that I've seen before include "People who don't want certain food" , "Very strict vegetarians" , "Extreme vegetarians" , "They eat no animal products" .)