Part of book for cathedral's governing body (7)
I believe the answer is:
chapter
'part of book' is the definition.
(many books contain chapters)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for chapter that I've seen before include "Episode" , "Book division - assembly of canons" , "Distinctive period of history" , "Division of book, usually numbered" , "Sequence - section of book - church body" .)