A slight cold contributing to much illness (5)
I believe the answer is:
chill
'a slight cold' is the definition.
(I've seen this before)
'contributing to much illness' is the wordplay.
'contributing to' says the answer is hidden in the clue (the answer contributes to part of the clue ).
'CHILL' can be found hidden inside 'much illness'.
(Other definitions for chill that I've seen before include "Slang injunction to relax - it's cold" , "Preserve by cold" , "Make cooler" , "Iciness" , "Unpleasent coldness in the air" .)