When Rush ‘s Geddy Lee first encountered Anika Nilles via YouTube, he immediately recognized that she wasn’t just a singularly capable drummer who happened to specialize in odd time signatures, but also a star in her own right. “I was like, ‘Oh, my God, she’s so good,'” Lee told Rolling Stone . “She’s so interesting, and she’s got such charisma, personal charisma, and flair.” Nilles had little idea of the brutal amount of work that lay ahead when Lee and Alex Lifeson first asked her to come to a studio in Toronto last year and play some Rush songs — and she couldn’t imagine the worshipful reception she’d end up getting from the band’s fans.

The German-born Nilles, 43, was serious about drumming as a kid, but her parents insisted she pursue more practical work, so she studied social work and got a job at a preschool. When she was 26, she changed her mind, and went back to school to study music, fearing it was too late.…