Special cart distributed church's cash (7)
I believe the answer is:
scratch
'cash' is the definition.
(thesaurus)
'special cart distributed church's' is the wordplay.
'special' becomes 's' (common abbreviation as in Special Air Service).
'distributed' indicates anagramming the letters.
'church' becomes 'ch' (common abbreviation).
'cart' with letters rearranged gives 'crat'.
's'+'crat'+'ch'='SCRATCH'
(Other definitions for scratch that I've seen before include "Handicap where expected to make" , "Don't play" , "Fail to start" , "Old Nick" , "Rough and ready" .)