Overheard one of two church administrators possibly supplying opiate (7)
I believe the answer is:
codeine
'opiate' is the definition.
(thesaurus)
I don't understand the remainder of the clue.
(Other definitions for codeine that I've seen before include "Common opium-based tablet used to relieve pain" , "Mild narcotic used as a pain-killer" , "Painkiller derived from opium" , "Niece, do take this drug" , "An anodyne" .)