Faint, not very fit (4)
I believe the answer is:
ague
'fit' is the definition.
(I've seen this before)
'faint not very' is the wordplay.
'faint' becomes 'vague'.
'not' is a deletion indicator.
'very' becomes 'v' (abbreviation).
'vague' with 'v' taken out is 'AGUE'.
(Other definitions for ague that I've seen before include "Old word for fever" , "Fever with shivers" , "Complaint" , "Malarial fever or fit of shivering" , "Fit of shivering and shaking" .)