Big-headed American's vehicle (3)
I believe the answer is:
bus
'vehicle' is the definition.
(bus is a kind of vehicle)
'big-headed american's' is the wordplay.
'big-headed' becomes 'b' (this could be a standard abbreviation I've not previously seen).
'american' becomes 'us' (abbreviation for United States).
'b'+'us'='BUS'
Can you help me to learn more?
(Other definitions for bus that I've seen before include "Road vehicle able to carry many passengers" , "Charabanc" , "Mode of public transport" , "Public transport vehicle" , "Use transport" .)