Relative's regularly inside church (5)
I believe the answer is:
niece
'relative's' is the definition.
(niece is a kind of relative)
'regularly inside church' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'church' becomes 'ce' (abbreviation for Church of England).
The alternate letters of 'inside' are 'nie'.
'nie'+'ce'='NIECE'
(Other definitions for niece that I've seen before include "Brother's daughter" , "[PRIEST'S] daughter?" , "A younger female relative" , "Brother's girl" , "Family relation" .)