People who lived in sin casually (4)
I believe the answer is:
inca
'people who lived' is the definition.
(historical South American civilization)
'in sin casually' is the wordplay.
'in' says the answer is hidden in the clue.
'INCA' is hidden within 'sin casually'.
(Other definitions for inca that I've seen before include "Member of ancient Peruvian tribe" , "member of historic race" , "Pre-conquest South American Indian" , "Old South American native" , "Ruler of an old empire centred on Cuzco" .)