Topless sport's producing illness (7)
I believe the answer is:
rickets
'illness' is the definition.
(rickets is a kind of illness)
'topless sport's' is the wordplay.
'topless' means to remove the first letter.
'sport's' becomes 'crickets' (cricket is a kind of sport).
'crickets' with its initial letter removed is 'RICKETS'.
'producing' is the link.
(Other definitions for rickets that I've seen before include "Childhood disease caused by a deficiency of vitamin D" , "Bone-distorting disease" , "Bone disease, caused by vitamin D deficiency" , "Children's disease" .)