The use of nitrate or sulfate to produce cellular energy is an example of

Anaerobic respiration

Explanation:

All living organisms need energy for their life processes. Some organisms utilize oxygen to break down organic molecules (aerobic respiration) while some archaea and bacteria that live in low-oxygen environment rely on anaerobic respiration to break down fuels.

Anaerobic respiration is the process of producing cellular energy without oxygen. Anaerobic respiration is similar to aerobic respiration in the sense that electrons from a fuel molecule are passed through an electron transport chain driving ATP synthesis, but instead of using oxygen (aerobic) as a terminal electron acceptor, alternate inorganic acceptors (elements) like nitrate, sulphate, Carbondioxide etc. are used.

For example, sulfate-reducing bacteria and Archaea use sulfate as a terminal electron acceptor, producing hydrogen sulfide (H2S) as a byproduct.