Cheerfully banning book with good reason (7)
I believe the answer is:
rightly
'with good reason' is the definition.
(I've seen this before)
'cheerfully banning book' is the wordplay.
'cheerfully' becomes 'brightly'.
'banning' suggests deleting specific letters.
'book' becomes 'b' (abbreviation for book).
'brightly' with 'b' taken out is 'RIGHTLY'.
(Other definitions for rightly that I've seen before include "With good reason" , "Justly, correctly" , "Justly, honestly" , "Honestly or justifiedly" .)