Self-satisfied hint of smile on face (4)
I believe the answer is:
smug
'self-satisfied' is the definition.
('smug' can be a synonym of 'self-satisfied')
'hint of smile on face' is the wordplay.
'hint of' indicates taking the first letters.
'on' is a charade indicator (letters next to each other).
'face' becomes 'mug' (mug is a kind of face**).
The initial letter of 'smile' is 's'.
's'+'mug'='SMUG'
(Other definitions for smug that I've seen before include "Steal" , "Unctuous" , "Irritatingly self-satisfied" , "Superior" , "Self-righteously complacent" .)