Illness going round place causes upset (9)
I believe the answer is:
displease
'upset' is the definition.
(thesaurus)
'illness going round place' is the wordplay.
'illness' becomes 'disease' (disease is a kind of health problem).
'going round' indicates putting letters inside (some letters go around others).
'place' becomes 'pl' (abbreviation used in postal addresses).
'disease' going around 'pl' is 'DISPLEASE'.
'causes' acts as a link.
(Other definitions for displease that I've seen before include "Vex" , "Aggravate" , "Upset" , "Anger" , "Nettle" .)