Frost’s father Doug coached Olympic swimming champion Thorpe at his Doug Frost Swim School from 1995.
Thorpe won eight Olympic medals in the pool, including five golds.
Detectives from the Child Abuse and Sex Crimes Squad were involved in assisting with inquiries, and the man is currently being questioned by police.
Paul Frost, who is married with children, worked at the swim school part-time at the time of the alleged assaults. He was also employed as a casual lecturer at the University of NSW for a time and as a casual teacher in 2016 by the NSW Department of Education.
He did not apply for bail and was formally refused bail. He will return to Sutherland Court on September 26.
He is the second swim school instructor arrested in Sydney in the past year on child sex allegations.
Mosman swim coach Kyle James Henk Daniels, 20, is currently facing 26 charges in relation to the alleged indecent assault of nine girls aged between five and 10 years.