Cleaner concealing private part of book (7)
I believe the answer is:
chapter
'part of book' is the definition.
(I've seen this before)
'cleaner concealing private' is the wordplay.
'cleaner' becomes 'char' (charwoman is a type of cleaner).
'concealing' means one lot of letters goes inside another.
'private' becomes 'pte'.
'char' going around 'pte' is 'CHAPTER'.
(Other definitions for chapter that I've seen before include "Cathedral body" , "Part of book" , "Division of written work" , "religious assembly" , "reading- matter" .)