"Reno-era" refers to the time when Janet Reno was the Attorney General of the US.
The second sentence of the Washington Post article mentions "then-Attorney General" Reno
Put in place by then-Attorney General Janet Reno, the policy prohibited the military from reporting certain drug abusers to the FBI, which manages the national list of prohibited gun-buyers, federal officials said.
Janet Reno is a former Attorney General of the United States (1993–2001). She was nominated by President Bill Clinton on February 11, 1993, and confirmed on March 11. She was the first female Attorney General and the second longest serving Attorney General after William Wirt.
EDIT: clarifed and moved WAPO article to top of answer