Inch falteringly behind relative in narrow passages (7)
I believe the answer is:
bronchi
'narrow passages' is the definition.
(passages within the body)
'inch falteringly behind relative' is the wordplay.
'falteringly' indicates an anagram.
'behind' says to put letters next to each other.
'relative' becomes 'bro' (short for brother).
'inch' is an anagram of 'nchi'.
'nchi' put after 'bro' is 'BRONCHI'.
'in' acts as a link.
(Other definitions for bronchi that I've seen before include "airy spaces" , "In airways" , "pipes" , "breathers" , "Branches of the windpipe" .)