Bodies of fools supporting motor clubs (9)

'bodies' is the definition.
(carcass is a kind of body)

'fools supporting motor clubs' is the wordplay.
'fools' becomes 'asses' (ass is a kind of fool**).
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'motor' becomes 'car' (I've seen this before).
'clubs' becomes 'c' (abbreviation used in card games such as bridge).
'car'+'c'='carc'
'asses' put after 'carc' is 'CARCASSES'.

'of' acts as a link.