Head of class unwell, nursing start of horrible cold (5)
I believe the answer is:
chill
'cold' is the definition.
(chill is a kind of cold)
'head of class unwell nursing start of horrible' is the wordplay.
'head of' says to take the initial letters.
'unwell' becomes 'ill' (similar in meaning).
'nursing' means one lot of letters goes inside another.
'start of' indicates taking the first letters.
The initial letter of 'class' is 'c'.
The initial letter of 'horrible' is 'h'.
'c'+'ill'='cill'
'cill' enclosing 'h' is 'CHILL'.
(Other definitions for chill that I've seen before include "Make cooler" , "Sensation of cold or dread" , "This disheartens" , "Slang injunction to relax - it's cold" , "Make cold (or frightened)" .)