Nerve is a related term of arrogance.
As a verb nerve
is .
As a noun arrogance is
the act or habit of arrogating, or making undue claims in an overbearing manner; that species of pride which consists in exorbitant claims of rank, dignity, estimation, or power, or which exalts the worth or importance of the person to an undue degree; proud contempt of others; lordliness; haughtiness; self-assumption; presumption.