Clergyman doesn't finish the right-hand page (5)
I believe the answer is:
recto
'right-hand page' is the definition.
(right-hand page of a book)
'clergyman doesn't finish' is the wordplay.
'clergyman' becomes 'rector' (rector is a kind of clergyman).
'doesn't finish' means to remove the last letter.
'rector' with its final letter taken off is 'RECTO'.
'the' is the link.
(Other definitions for recto that I've seen before include "The right-hand page or leaf of a book" , "Side of paper" , "right page" , "Right-hand page of an open book" , "Odd-numbered page" .)