Adverbial use of the te-form of 急ぐ, describing doing something quickly or in haste.
I left the house in a hurry.
hurry up!; quickly!; get going!
Used as an interjection to urge someone to act quickly. Often used alone or at the beginning of a sentence.
Hurry up! The train is leaving.
Please don't eat in a rush.
急いで describes the hurried manner of doing an action, while 急に more often describes a sudden change or something forced by unexpected circumstances.
急いで means doing something hastily, whereas ゆっくり means doing something slowly and calmly.
The te-form of the verb 急ぐ (to hurry), used as an adverb or interjection.