Conceited introduction of smiley face (4)
I believe the answer is:
smug
'conceited' is the definition.
(I've seen this before)
'introduction of smiley face' is the wordplay.
'introduction of' suggests taking the first letters.
'face' becomes 'mug' (informal term for face).
The initial letter of 'smiley' is 's'.
's'+'mug'='SMUG'
(Other definitions for smug that I've seen before include "Unpleasantly complacent" , "Be envious of" , "irritating expression" , "Irritatingly self-satisfied" , "goody-goody" .)