Robin flying around church's inner passages (7)
I believe the answer is:
bronchi
'inner passages' is the definition.
(air passages in the lungs)
'robin flying around church's' is the wordplay.
'flying' indicates an anagram (letters fly around into new positions).
'around' indicates putting letters inside.
'church' becomes 'ch' (common abbreviation).
'robin' is an anagram of 'broni'.
'broni' going around 'ch' is 'BRONCHI'.
(Other definitions for bronchi that I've seen before include "Air passages" , "pipes" , "airlines" , "Branches of the windpipe" , "In airways" .)