AR stands for Age of Rouvenor, an era within the history of the Ethnic Gallente. From the article:
Doule dos Rouvenor III inherited his father’s crown in 21714AD, and started a new calendar based on his ascension, the Age of Rouvenor (AR). An AR year is 1.21 of its pre-Yoiul equivalent, and is still used in many places on Gallente Prime.
There’s also the Federal Calendar, or FC, which started when the Federated Union of Gallente Prime was signed into existence. It’s currently FC238 iirc.