One following strict diet, say, squeezed into vehicle (5)
I believe the answer is:
vegan
'one following strict diet' is the definition.
'say squeezed into vehicle' is the wordplay.
'say' becomes 'eg' (short for 'exempli gratia', 'for example' in Latin).
'squeezed into' means one lot of letters goes inside another.
'vehicle' becomes 'van' (van is a kind of vehicle).
'eg' put into 'van' is 'VEGAN'.
(Other definitions for vegan that I've seen before include "One not eating animals" , "Person refraining from using animal products in any way" , "One avoiding all animal-based food" , "An extreme vegetarian" , "Person neither eating nor using anything animal" .)