With the brass band revival in full swing, Treme vets James Andrews, Kirk Joseph, Benny Jones and Lionel Batiste come together with their protégés to keep traditional street music marching forward.

“Brass Band music will always be played here,” says Benny Jones, Sr., the 52-year-old snare drummer and leader of the Treme Brass Band, leaning forward in his chair as he cools off with a sip of beer. He’s referring to the band’s name...