Hacienda operated with support of church (5)
I believe the answer is:
ranch
'hacienda' is the definition.
(thesaurus)
'operated with support of church' is the wordplay.
'operated' becomes 'ran' ('run' can be a synonym of 'operate').
'with' means one lot of letters go next to another.
'support of church' becomes 'ch' (I've seen this in other clues).
'ran'+'ch'='RANCH'
(Other definitions for ranch that I've seen before include "Stock farm in US, Aus." , "stock holding?" , "Hacienda" , "Run a cattle farm" , "Large farm rearing particular livestock" .)