Falsehood about fine biography (4)
I believe the answer is:
life
'biography' is the definition.
(synonyms)
'falsehood about fine' is the wordplay.
'falsehood' becomes 'lie' (lie is a kind of falsehood).
'about' indicates putting letters inside.
'fine' becomes 'f' (abbreviation in pencil classifications).
'lie' placed around 'f' is 'LIFE'.
(Other definitions for life that I've seen before include "Maximum stretch?" , "Baffin oiler (anag) - 7 film" , "The longest sentence" , ""But an empty dream" (Longfellow) - "As tedious as a twice-told tale" (Shakespeare)" , "Animation" .)