Falsehood about fine biography (4)
I believe the answer is:
life
'biography' is the definition.
(I know that biography can be written as life)
'falsehood about fine' is the wordplay.
'falsehood' becomes 'lie' (lie is a kind of falsehood).
'about' means one lot of letters goes inside another.
'fine' becomes 'f' (abbreviation in pencil classifications).
'lie' going 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" .)