Agricultural Emergency Relief Act of 2023 This bill directs the Department of Agriculture (USDA) to establish an Emergency Relief Program to provide payments each crop year to producers that experience a qualified loss as a result of a disaster that occurred during the crop year. (Under current law, USDA provides payments under a temporary Emergency Relief Program for losses that occurred following disasters in 2020, 2021, or 2022.) The bill defines a qualified loss as a loss incurred by a producer in a crop, trees, bushes, or vines as a consequence of a disaster (i.e., a drought, wildfire, hurricane, flood, derecho, excessive heat, excessive moisture, a winter storm, and a freeze event, including a polar vortex). Further, a qualified loss includes a loss incurred as a result of being prevented from planting a crop due to a disaster and a loss in the quality of a crop, trees, bushes, or vines due to a disaster or smoke exposure from a wildfire. As a condition of receiving a payment under this program, a producer must purchase (for the next two years) Federal Crop Insurance or, if Federal Crop Insurance is not available, coverage under the Noninsured Crop Disaster Assistance Program. An eligible producer under the program is an individual or entity that is eligible to receive assistance under a Farm Service Agency administered disaster assistance program. The bill specifies that a producer does not include a joint venture or a general partnership.