Car: one crashed following councillor bagging it (7)

'car' is the definition.

'one crashed following councillor bagging it' is the wordplay.
'crashed' indicates an anagram.
'following' means one lot of letters go next to another.
'councillor' becomes 'cr' (I've seen this in other clues).
'bagging' is an insertion indicator (I've seen this in other clues).
'one' is an anagram of 'oen'.
'oen' put after 'cr' is 'croen'.
'croen' placed around 'it' is 'CITROEN'.