Inspector lifted rule, overseeing one religious festival (6)
I believe the answer is:
diwali
'religious festival' is the definition.
(I've seen this before)
'inspector lifted rule overseeing one' is the wordplay.
'inspector' becomes 'di' (abbreviation for Detective Inspector).
'lifted' shows that the letters should be reversed in order (going up in down clue).
'rule' becomes 'law' (law is a kind of rule).
'overseeing' means one lot of letters go next to another (in a down clue, some letters go over others).
'one' becomes 'i' (Roman numeral).
'law' backwards is 'wal'.
'di'+'wal'+'i'='DIWALI'
(Other definitions for diwali that I've seen before include "Hindu festival; I'd wail (anag.)" , "Hindu festival of lights" , "Festival in honour of Lakshmi" , "Indian festival" , "Light festival" .)