A scream -- under church carriage! (7)
I believe the answer is:
chariot
'carriage' is the definition.
(chariot is a kind of carriage)
'a scream under church' is the wordplay.
'scream' becomes 'riot' ('riot' can be a synonym of 'scream'**).
'under' is a charade indicator (letters next to each other).
'church' becomes 'ch' (common abbreviation).
'a'+'riot'='ariot'
'ariot' put after 'ch' is 'CHARIOT'.
(Other definitions for chariot that I've seen before include "four-wheeled carriage?" , "former military vehicle" , "Two-wheeled carriage of ancient times, as used by Ben Hur" , "Haricot (anag)" , "Two-wheeled horse-drawn vehicle used in battle" .)