Better Collaboration, Accountability, and Regulatory Enforcement for Animals Act of 2023 or the Better CARE for Animals Act of 2023 This bill modifies enforcement provisions under the Animal Welfare Act, including by allowing the Department of Justice (DOJ) to bring civil actions against violators of the act for appropriate relief, such as removing animals, revoking violators' licenses, or issuing civil penalties. DOJ must use the penalties to pay for the temporary care for animals pending the disposition of civil or criminal proceedings that allege violations of the act with respect to such animals.