Principal hospital supporting a church (4)
I believe the answer is:
arch
'principal' is the definition.
(thesaurus)
'hospital supporting a church' is the wordplay.
'hospital' becomes 'h'.
'supporting' means one lot of letters go next to another (in a down clue, some letters go below others).
'church' becomes 'rc' (abbreviation for Roman Catholic**).
'a'+'rc'='arc'
'h' after 'arc' is 'ARCH'.
(Other definitions for arch that I've seen before include "Structural curve" , "Knowing, sly" , "Curved spanning structure" , "which may fall and inconvenience walkers" , "spanner" .)