The New Breed Brass Band rolls at four major New Orleans festivals this year. In order of its appearances they include the Freret Street Festival, the French Quarter Festival, Jazz Fest and the Essence Festival. At OffBeat’s Best of the Beat Awards in January, the band won for Best Emerging Artist. Not bad for a group that’s only been around for about three years.

“It’s an honor for a band that’s just starting out,” agrees 25-year-old snare drummer Jenard Andrews, the son of trump...