Republican lodged in a bogus religious retreat (6)
I believe the answer is:
ashram
'religious retreat' is the definition.
(type of religious retreat in Asia)
'republican lodged in a bogus' is the wordplay.
'republican' becomes 'R' (abbreviation in US politics).
'lodged in' is an insertion indicator.
'bogus' becomes 'sham' (both can mean fake).
'a'+'sham'='asham'
'r' going into 'asham' is 'ASHRAM'.
(Other definitions for ashram that I've seen before include "Retreat -- a marsh (anag)" , "Guru's community" , "Indian hermitage" , "Place of religious retreat for Hindus" , "Hindu religious retreat" .)