Self-indulgent? It's proper embracing a daughter (8)
I believe the answer is:
decadent
'self-indulgent?' is the definition.
('decadent' can be similar in meaning to 'self-indulgent')
'proper embracing a daughter' is the wordplay.
'proper' becomes 'decent' ('decent' is associated in meaning with 'proper').
'embracing' means one lot of letters goes inside another.
'a daughter' becomes 'ad' (I've seen this in other clues).
'decent' placed around 'ad' is 'DECADENT'.
'it's' is the link.
(Other definitions for decadent that I've seen before include "base?" , "Reprobate" , "Decanted in corrupt way" , "Luxuriously self-indulgent" , "Self-indulgent or immoral" .)