Your disc probably has day and night cycles. If the sun always follows the same path over and over, then seasons don't exist, and therefore neither do solar years. If the moon is also unchanging then there are no lunar years either. If so, years will be completely arbitrary and based on whatever people had on their minds when coming up with stuff, just like the imperial system.
Some people might count years in groups of a hundred days, because a hundred were the sneezes that saint Incognito let put before he died. But some people will count the year as 314.16 days, because the world is a disc and the number π is holy. Also leap days in this latter system are a mess.
If the sun's path does tilt one way or another, ciclically, you have seasons. A solar year will be completed when the sun is done.
Similarly, if the moon has phases or a tilting path, you have lunar years.
You could also get some inspiration from the Discworld, but in that case the disc does revolve. On top of that most people living on the disc hate astrologers and astrologers hate the gods due to the inherent chaos that is the motion of their stars.