Writer of one's biography written up (5)
I believe the answer is:
ibsen
'writer' is the definition.
(Ibsen is an example)
'of one's biography written up' is the wordplay.
'of' indicates a hidden word.
'written up' is a reversal indicator.
'nesbi' can be found hidden inside 'ones biography'.
'nesbi' written backwards gives 'IBSEN'.
(Other definitions for ibsen that I've seen before include "6 24 113 [SCAN-DIN-AVIAN] writer" , "Norwegian dramatist, Henrik (1828-1906)" , "Noted Norwegian playwright" , "Hedda Gabler author" , "See 7 Down" .)