Head off unspecified fever (4)
I believe the answer is:
ague
'fever' is the definition.
(I've seen this before)
'head off unspecified' is the wordplay.
'head off' means to remove the first letter.
'unspecified' becomes 'vague'.
'vague' with its initial letter removed is 'AGUE'.
(Other definitions for ague that I've seen before include "met with cheek in Twelfth Night" , "Feverish illness" , "Sweating, shivering, fit (once)" , "Fit of shivering and shaking" , "Feverish chill" .)