Grijalva was a champion of environmental protections and reliably went to bat for immigrants and Native American tribes.

Voters in southern Arizona are selecting nominees Tuesday to succeed the late U.S. Rep. Raúl Grijalva, who was one of the most senior and progressive power brokers on Capitol Hill.

Adelita Grijalva entered the race as the front-runner and garnered the lion’s share of endorsements in the contest, including support from both of Arizona’s US senators as well as Vermont Sen. Bernie...