Conservatives backed naked foray into places of prayer (9)
I believe the answer is:
oratories
'places of prayer' is the definition.
(I've seen this in another clue)
'conservatives backed naked foray' is the wordplay.
'conservatives' becomes 'Tories' (informal term for the Conservative Party).
'backed' means one lot of letters go next to another (some letters go at the back of others).
'naked' indicates the central letters (outside letters removed so centre is unclothed).
The centre of 'foray' is 'ora'.
'tories' put after 'ora' is 'ORATORIES'.
'into' acts as a link.
(Another definition for oratories that I've seen is " places of worship".)