Religious service affecting godliness? Not the first third of it (6)

I believe the answer is:

ritual

'religious service' is the definition.
'ritual' can be an answer for 'service' (I've seen this before). I am not sure about the 'religious' bit.

I can't explain the remainder of the clue.

(Other definitions for ritual that I've seen before include "Habits" , "Custom, rite" , "Prescribed ceremonial procedure" , "Regular habit" , "Code of ceremonies" .)

I've seen this clue in The Guardian.

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Religious service affecting godli­ness? Not the first third of it (6)

Religious service affecting godliness? Not the first third of it (6)