Series absorbs ill-bred playwright (10)
I believe the answer is:
strindberg
'playwright' is the definition.
(I know that Strindberg is a playwright)
'series absorbs ill-bred' is the wordplay.
'series' becomes 'string' (sequence of similar items or events).
'absorbs' means one lot of letters goes inside another.
'ill' is an anagram indicator.
'bred' is an anagram of 'dber'.
'string' going around 'dber' is 'STRINDBERG'.
(Other definitions for strindberg that I've seen before include "August --, dramatist" , "playwright" .)