Hiding cold at one time, illness I avoided (11)
I believe the answer is:
concealment
'hiding' is the definition.
(synonyms)
'cold at one time illness i avoided' is the wordplay.
'cold' becomes 'C' (eg on taps).
'at one time' becomes 'once' (both can mean 'in the past').
'illness' becomes 'ailment' (an ailment is an illness or health problem).
'avoided' is a deletion indicator.
'ailment' with 'i' removed is 'alment'.
'c'+'once'+'alment'='CONCEALMENT'
(Other definitions for concealment that I've seen before include "Process of hiding" , "Hiding; secrecy" , "Act of hiding" , "Whitewash" .)