Playwright's woman managed to steal papers (8)
I believe the answer is:
sheridan
'playwright's' is the definition.
(I've seen this before)
'woman managed to steal papers' is the wordplay.
'woman' becomes 'she' ().
'managed' becomes 'ran' (I've seen this before).
'to steal' means one lot of letters goes inside another.
'papers' becomes 'id' (identification papers).
'ran' enclosing 'id' is 'ridan'.
'she'+'ridan'='SHERIDAN'
(Other definitions for sheridan that I've seen before include "School for Scandal playwright" , "Irish dramatist" , "Richard Brinsley . . . . . . . . was a great 18th century Irish playwright" , "The Rivals author" , "Irish playwright and politician, d. 1816" .)