Conceited, puffed-up (4)
I believe the answer is:
vain
I believe this is a double definition.
'conceited' is the first definition.
(I know that conceited can be written as vain)
'puffed-up' is the second definition.
(I've seen this in another clue)
(Other definitions for vain that I've seen before include "Having too much pride in one's appearance" , "Having an exaggerated sense of self-importance" , "Useless; conceited" , "Forever looking in the mirror" , "Conceited, proud of appearance" .)