TL;DR:

With existing technology it’s tough to detect oxygen on smaller far-away planets. However, what we could instead look for is a combination of gases that likely means presence of life on earlier stages, before oxygen becomes abundant in the atmosphere. (The assumption is that the alien life we might find would likely be on early stages of development anyway.)

This research is about how such a combination of gases—lots of carbon dioxide, methane, and no carbon monoxide—can be detected and told apart from possible nonliving sources. The new approach should be viable to apply using Webb telescope on smaller planets like the ones in TRAPPIST-1 system.