KABUL—Some former members of Afghanistan’s U.S.-trained intelligence service and elite military units—now abandoned by their American patrons and hunted by the Taliban—have enlisted in the only force currently challenging the country’s new rulers: Islamic State.

The number of defectors joining the terrorist group is relatively small, but growing, according to people who know these men, to former Afghan security officials and to the Taliban. Importantly, these new recruits bring to Islamic State critical expertise in intelligence-gathering and warfare techniques, potentially strengthening the extremist organization’s ability to contest Taliban supremacy.