Whilst there, in 1965 he founded the Chapter House Choir, a mixed voice ensemble that achieved national renown under his direction of seventeen years.
After spending a year conducting and adjudicating in New Zealand (1984), he returned to England to focus on composition.
Oxford University Press have published more than fifty of his compositions over a period of association spanning twenty-five years.
A notable moment in Carter's musical career was a commission in 1997 to write a mass (Missa Sancti Pauli) for the tercentenary celebration of St Paul's Cathedral in London.
In 2007, he composed a 22-variation passacaglia for organ to mark the 90th birthday of the former York Minster organist Francis Jackson.