The Football Association backs just business (6)
I believe the answer is:
affair
'business' is the definition.
(I've seen this in another clue)
'the football association backs just' is the wordplay.
'the football association' becomes 'FA' (abbreviation).
'backs' shows that the letters should be reversed in order.
'just' becomes 'fair' (just can mean fair in the sense of showing justice).
'fa' back-to-front is 'af'.
'af'+'fair'='AFFAIR'
(Other definitions for affair that I've seen before include "A function or a romance" , "Secret liaison" , "A fling (or something more serious?)" , "See 23" , "Matter or concern, perhaps of the heart" .)