Self-important (4)
'self-important' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for pompous that I've seen before include "Affectedly grand" , "Arrogant" , "Grandiose" , "Grandiloquent" , "Proud" .)
'self-important' is the definition.
(thesaurus)
This is the entire clue.
(Other definitions for vain that I've seen before include "Conceited - or a waste of time" , "Conceited or pointless" , "Useless; self-regarding" , "Conceited or unsuccessful" , "Egotistical" .)