The second man faces a raft of similar charges - 21 counts of indecent assault on young boys from under 12 up to and over 16.
Both men were remanded in jail until their next court hearings in December.
Browne is currently serving a six-and-a-half-year jail sentence for abusing students at the Auckland School between 1987 and 1992.
He was appointed chaplain at Dilworth School in October 1979, where he was responsible for religious education.
At the time of his arrest in September 2020, he was the vicar of St Luke’s Church in Manurewa.
He had also been involved in Scouts and amateur theatrical company the Auckland Gang Show.
Browne pleaded guilty in October to 15 charges involving 14 children and adolescents who were abused between 1987 and 2002.
Most of the victims were between the ages of 12 and 16. He received concurrent six-and-a-half-year sentences for each of the charges.
In addition, he was ordered to serve a concurrent one-year sentence for possession of objectionable publications depicting child abuse that were found when police searched his home in 2020.
At least 12 men have been arrested and charged since police began looking into allegations of historic sexual offending at Dilworth School.
Several of those men are now serving time.
The private boarding school in Auckland has set up a redress scheme for the survivors and commissioned an Independent Inquiry, headed by Dame Silvia Cartwright, into the abuse.
A large group of former students are also taking a class-action suit against the school.
