This was known as the Fremantle Port Authority building when new in 1963.
I took this photo from what is now the boardroom of the MSC Dalgety building on the corner of Cliff and Phillimore Streets. The Fremantle Ports building uses the street address 1 Cliff St, tho it's not really in Cliff St, which ends where I took this photo, at the corner of Phillimore St. The Ports building is actually between the former anonymous entrance to Victoria Quay which is now known as Peter Hughes Drive (who does it have two names?) and Slip St, which leads to two slipways, on one of which is the Ovens submarine.
The building was designed by Hobbs, Winning & Leighton, the firm founded by J.J. Talbot Hobbs, who also designed the Dalgety building from which, as I say, I took this photo. The firm also designed the Passenger Terminal (1962) on Victoria Quay.
The building on this site before 1962 was the Harbour Trust building, which itself was formerly at Arthur Head on the western end of what became the southern wharf, and served as C.Y. O'Connor's office.
Fremantle Ports is plural because it controls not only the port in the Swan River, but also various facitilities in Cockburn Sound. It has a board of directors appointed by and responsible to the Minister for Transport, and a Chief Executive Officer appointed by the Board who is responsible for day-to-day management. Currently it's (male) Chris Leatt-Hayter. The previous incumbent is now the Governor of Western Australia, (female) Kerry Sanderson.
Fremantle Ports website
Garry Gillard | New: 17 September, 2017 | Now: 24 September, 2017