Reduce a part of the nose (7)
I believe the answer is:
abridge
'reduce' is the definition.
('abridge' can be a synonym of 'reduce')
'a part of the nose' is the wordplay.
'part of the nose' becomes 'bridge' ('bridge' is part of 'nose').
'a'+'bridge'='ABRIDGE'
(Other definitions for abridge that I've seen before include "Big read (anag) - shorten text" , "Make shorter, book say" , "Shorten, a book say, without losing the sense" , "Make short work" , "Crop" .)