DUBAI—America’s Gulf Arab allies are stepping up their involvement in Afghanistan, expanding their diplomatic existence and resuming flights as opposition for influence above the new Taliban administration heats up.

Qatar, which housed the Taliban’s political place of work for various many years and served as the location for the Islamist movement’s peace talks with the U.S., capitalized on that influence to come to be a crucial conduit between Afghanistan and the West following the Taliban seized energy on Aug. fifteen.