ANE is an abbreviation which stands for “Ancient Near East.” The term does not appear in the Bible but is often used by scholars when discussing Bible passages and the life and times of Bible days, particularly the Old Testament.
The Ancient Near East, geographically is what we commonly refer to as the Middle East today. Usually when ANE appears however, it is not in reference to a geographical region. Instead, it is typically used in reference to the cultural practices of the people of that region in that era of time.
One might commonly see ANE used in a reference such as “Treaties in the ANE were often sealed through a blood sacrifice.” In Bible related terms, ANE is usually referenced to show either that Israel’s practices were common among many people of the day or that God had instituted practices that were quite counter to common practices of the day.