Writer of one's biography in the ascendancy (5)
I believe the answer is:
ibsen
'writer' is the definition.
(Ibsen is an example)
'of one's biography in the ascendancy' is the wordplay.
'of' indicates the answer is hidden within the clue.
'in the ascendancy' shows that the letters should be reversed in order (in a down clue, letters go up or ascend).
'nesbi' can be found hidden inside 'ones biography'.
'nesbi' reversed gives 'IBSEN'.
(Other definitions for ibsen that I've seen before include "Is Ben a playwright?" , "Norwegian dramatist of 'Hedda Gabler'" , "'Doll's House' playwright" , "Norwegian playwright, d. 1906" , "Playmaker" .)