No, neon tetras do not need an air pump. Neon tetras don’t need extra oxygen pumped into their tank and will still thrive without an air pump.
However, neon tetras do require 12–14 hours of light during the day, every day. They also need an aquarium filter, a big enough tank, an aquarium heater (to keep the water temperature between 73 and 79 degrees Fahrenheit (23–26 degrees Celsius)), a PH level of between 5.5 and 6.8, clean living conditions, and to be kept in a school of a minimum of six members.