Hyde was born in the U.K. in 1980. As with so many other figures in the world of English choral music, he began his career as a boy chorister, enrolling in the Durham Cathedral chorister school at age seven. Hyde's career as a boy singer was cut short when his voice broke, a year before he was set to leave the Durham choir, so he took up the organ instead. By 17, he was already an organ scholar (an organist who furnishes music for services in exchange for tuition reductions) at Durham Cathedral and a fellow of the Royal College of Organists. He worked for a year as the assistant organist at Perth Cathedral in Australia before becoming an organ scholar at King's College, Cambridge, in 2000. Hyde won two prizes at the Royal College of Organists Performer of the Year Competition in 2002 and graduated from King's College with first-class honors the following year. Hyde was soon hired as director of music at Jesus College, Cambridge, and then in 2009, as choirmaster ("Informator Choristarum"), tutorial fellow, and lecturer at Magdalen College, Oxford. He has been a guest conductor with a variety of choirs and orchestras, including the BBC Singers (where he served as accompanist for a time), the London Bach Choir, and the Academy of St. Martin in the Fields. He moved to New York in 2016 to take a position as the organist and director of music at Saint Thomas Church Fifth Avenue in New York. In 2018, Hyde was named the director of music for the Choir of King's College, Cambridge, replacing the retiring Stephen Cleobury. He was slated to take up the baton in October of 2019 but stepped in early due to Cleobury's ill health, leading the choir on a tour of Australia.
Hyde has recorded as both an organist and choir director, beginning in 2007 with the album Christmas Organ Music from King's College, Cambridge. He has recorded for Priory, Naxos, Opus Arte, and other labels. In 2020, Hyde released the album Carols from King's.