Mensch started his career in music management at the age of 26, managing AC/DC. In 1982, he formed the management company Q Prime with Cliff Burnstein. Their first client was Def Leppard. Q Prime has managed the careers of a large number of multiplatinum acts; including Metallica and Red Hot Chili Peppers, Muse, Smashing Pumpkins, Hole, Veruca Salt, Snow Patrol and many others, including Jimmy Page. The Financial Times has called Q Prime "One of the most admired artist management companies".
His sister, Barbara Sena Mensch, was the youngest hostage of the Dawson's Field hijackings of September 6, 1970. Mensch graduated from Scardsdale High School in 1971. He attended Brandeis University and worked as a music director for the college radio station, which is where he met Cliff Burnstein. After graduating from Brandeis, he received his master's degree in Marketing from the University of Chicago.
Mensch began his professional career after graduating from the University of Chicago. His first assignment was as a label manager with Blank Records in New York. Shortly thereafter, he joined mega-talent firm, Leber-Krebs, as a tour accountant. He worked with such acts as Aerosmith and Scorpions. As a tour accountant with Aerosmith Mensch came upon the Australian rock band AC/DC, and persuaded them to swap their previous manager, Michael Browning, for Leber-Krebs. Mensch was assigned to manage the band as his first client; he was 26 years old.
On the advice of his friend Cliff Burnstein, then at Mercury Records, Mensch targeted the British group Def Leppard. He booked the band as support act on an AC/DC tour. A BBC documentary on the band records their unhappiness with their early managers Pete Martin and Frank Stuart-Brown, following a fist-fight between singer Joe Elliott and Martin. The film quotes Mensch as saying Burnstein told him "I don't care if they have managers...steal them from another set of managers." The band's drummer Rick Allen recollects that he did approach Mensch, and Mensch signed them to Leber-Krebs. After a disagreement with Leber-Krebs over royalties, Mensch was terminated from that firm and started Q Prime with Cliff Burnstein. Def Leppard was the sole client to come with the new firm.
Q Prime management made their name in heavy metal music, managing, at various times, AC/DC, Scorpions, Def Leppard, Dokken, Tesla, Suicidal Tendencies, Queensrÿche, and Metallica. In the early nineties their roster expanded to include alternative rock bands such as The Smashing Pumpkins, Hole, and Veruca Salt. They co-managed Madonna for one album, Ray of Light, and also consulted for the Rolling Stones on their Steel Wheels Tour in 1990. They managed Led Zeppelin for their reunion show, and Jimmy Page as a solo artist for several years after that. They have also managed Shania Twain for part of her career. The firm's present roster includes Metallica, the Red Hot Chili Peppers, Muse, Snow Patrol, Foals, Silversun Pickups, Cage the Elephant, Dawes and others. They additionally manage country acts from their Q Prime Nashville imprint, including Eric Church and Gillian Welch, and the Black Keys. They managed the opera singer Renée Fleming for her crossover album Dark Hope.
According to an interview with The Sunday Times, Mensch stated that he had assisted with the sale of "Hundreds of millions" of records, adding "I can't be more specific than that." In 2014, he did not return to manage AC/DC, but hinted that the band were to headline the Saturday night at Glastonbury Festival in 2015.
Mensch married Su Wathan, former girlfriend of Gary Numan, in 1981. He has three children by his second wife, Melissa Meyer, whom he divorced in 2010. The divorce was contentious. On February 17, 2011 in Manhattan courthouse  he married his third wife, Louise Mensch, former member of British Parliament, despite their political differences (Louise alleges that Peter is a communist). Louise subsequently became widely known in the US for her reporting and speculation about connections between Trump administration and the Russian government.
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One upside of l'affaire Trump is that Mensch — a lifelong Tory — and her husband, whom she describes as a 'f****** commie', are in rare agreement over politics.