There are multiple definitions - click on the translation that matches your context.

Auftrag

Substantiv

partial

contract

noun

Comparative law notes

Germany

If Auftrag is used in the sense of a job that has already been awarded to a contractor (and is therefore "under contract"), the proper English translation would be the loosely used English term "contract".

Definitions of contract

English

a negotiated and legally binding arrangement between two or more parties.

The contract was signed yesterday.