Walk with an air of self-importance (7)
I believe the answer is:
swagger
'walk with an air of self-importance' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for swagger that I've seen before include "Walk proudly" , "Proud, pompous gait" , "Blustering arrogance" , "Walk arrogantly" , "Lofty proud gait" .)