Old Republican is supported by prayer (6)
I believe the answer is:
Here is my best explanation:
'prayer' is the definition.
('orison' can be a synonym of 'prayer')
'old republican is supported by' is the subsidiary indication.
'old' becomes 'o'.
'republican' becomes 'r' (abbreviation).
'supported by' becomes 'on'.
(Other definitions for orison that I've seen before include "O, no, sir, it makes a prayer", "Prayer - O no sir! (anag)", "Supplication", "Prayer (archaic)" and "An archaic or literary prayer".)