Church district not completely in capital (5)
I believe the answer is:
paris
'capital' is the definition.
(capital of France)
'church district not completely' is the wordplay.
'church district' becomes 'parish' (area associated with a church).
'not completely' means to remove the last letter.
'parish' with its final letter taken away is 'PARIS'.
'in' acts as a link.
(Other definitions for paris that I've seen before include "European capital - Greek hero" , "Legendary prince" , "'''I love ... in the springtime'' (Cole Porter) (5)'" , "Eiffel Tower city" , "French department" .)