Child is sick, gets cold (5)
I believe the answer is:
chill
'cold' is the definition.
(chill is a kind of cold)
'child is sick' is the wordplay.
'child' becomes 'ch'.
'is sick' becomes 'ill' (similar in meaning).
'ch'+'ill'='CHILL'
'gets' acts as a link.
(Other definitions for chill that I've seen before include "minor illness" , "nip" , "Make cool" , "Preserve by cold" , "Sharp cold" .)