Traverse was a native of London and played with the Royal Opera House at Covent Garden. For seven years he performed at night while working in a day job in the British military. He later played with the Royal Philharmonic Orchestra, the London Philharmonic Orchestra, and the Royal Liverpool Philharmonic Orchestra.
Traverse joined the Houston Symphony in 1978. He was co-concertmaster until 1995 and resigned in 1997 due to Parkinson's disease, according to the Chronicle.
Traverse was also a composer, and his work was highlighted in February at the World Parkinson Congress in Washington, D.C.
He died of heart disease and Parkinson's disease.