Weapon has Mark stifle expression of self-importance (8)
I believe the answer is:
scimitar
'weapon' is the definition.
(scimitar is a kind of weapon)
'mark stifle expression of self-importance' is the wordplay.
'mark' becomes 'scar' (mark left by an injury).
'stifle' means one lot of letters goes inside another.
'expression of self-importance' becomes 'I'm it' ('I'm it' means 'I'm very important').
'scar' enclosing 'imit' is 'SCIMITAR'.
'has' is the link.
(Other definitions for scimitar that I've seen before include "This cut" , "Double-edged sword" , "Type of sword with curved blade" , "sharp weapon" , "I'm racist, owning an oriental sword" .)