(Comparably) tall building on Stanley Street completed in 1891 (mentioned in a comment here). The owner was A.S. Watson & Co. („Watson's Aerated Water Factory”)/the Hongkong Dispensary.
This building was constructed on the western part of the houses 36-40 Queen’s Road Central (QRC), likely on 40 (and maybe 38) QRC. The houses 36-40 QRC are all on I.L. 17, so is 1 Stanley Street. It looks as if the tall building has been constructed somewhat behind the existing buildings as the facade towards Queen's Road seems to be unchanged (see here Queen's Road looking west. Possibly they used the technique of keeping the façade and constructing a new building behind it.
This construction can be seen on these two photos showing the area from two different angles.
The building was likely demolished with the other buildings of 30-40 QRC around 1957, possibly a few years later. In 1965, Manning House (38-48 QRC) opened.