Falsehood raised by faculty head is a blow (4)
I believe the answer is:
biff
'blow' is the definition.
(I know that biff is a type of blow)
'falsehood raised by faculty head' is the wordplay.
'falsehood' becomes 'fib' (fib is a kind of falsehood).
'raised by' says the letters should be written backwards.
'head' indicates taking the first letters.
The initial letter of 'faculty' is 'f'.
'fib' in reverse letter order is 'bif'.
'bif'+'f'='BIFF'
'is a' is the link.
(Other definitions for biff that I've seen before include "Hard blow with fist" , "strike" , "Punch" .)