taru-adjective, adverb taking the 'to' particle
Literary word describing a proud, arrogant, or haughty attitude or manner. Often used as 傲然と or 傲然たる.
彼は傲然と胸を張って歩いた。
He walked with his chest puffed out proudly.
傲然たる態度で命令を下した。
He gave orders with a haughty attitude.
傲慢 is a more common word for arrogance, used as a na-adjective or noun. 傲然 is literary and often used adverbially.
The exact derivation is uncertain; the spelling is conventionally associated with pride and arrogance.