Perhaps church support aeronautics, though something hairy (6,8)
I believe the answer is:
flying buttress
'perhaps church support' is the definition.
(type of architectural support common in churches)
'aeronautics though something hairy' is the wordplay.
'aeronautics' becomes 'flying' (aeronautics is the field of flying).
'though' becomes 'but'.
'something hairy' becomes 'tress' (a tress is a lock of hair).
'flying'+'but'+'tress'='FLYING BUTTRESS'
(Other definitions for flying buttress that I've seen before include "Arch" , "support?" , "Big prop" , "Architectural feature" , "part of church?" .)