Though described as a temporary pier, it was here for over 16 years.
Notes from Moddsey on http://gwulo.com/node/7000#comment-14020:
In November 1892, a contract was signed for the construction of a temporary pier opposite Ice House St for the purposes of accommodating ferry and other traffic plying from Pedder's Wharf and constructing Section No. 7 of the praya reclamation works.
On 27 June 1894, the temporary timber wharf opposite Ice House St ((ie this pier)) was opened to traffic and the wharf known as Pedder's Wharf was closed.
In 1900 the Ice House Street Wharf was leased to the Star Ferry Co. on the completion of Blake Pier.
It looks as though the pier was for the sole use of the Star Ferry from 1900 onwards. I guess they also used it between 1894 and 1900, sharing it with other boats & launches.
Demolition date is approximate - see details of the later Star Ferry pier at this site for details.
From the Public Works Report for 1894
97. The temporary wharf opposite Ice House Street, contract No.15/1892 was after many delays and difficulties completed and opened to traffic on the 27th June. The timber required in its construction having been lost in the wreck of the Penshaw on a voyage from Manila to Hongkong on the 21st February, 1893, and a fresh supply had to be ordered by CHAN A TONG, the Contractor.