This was the second post office for TST, see Moddsey's notes below. There's a building in about the right position in this 1900's photo, but it's not clear if it's exactly the same one:
It was definitely there in 1910, as it appears in this photo of the first train leaving TST on 1st Oct that year. Here are another couple of views from the 1910's:
Possibly it was built around the same time as the railway terminus, which was just across the road.
From this site the Post Office moved to a larger building across the street, next to the railway terminus.
I'm not sure when the old building was finally demolished. It looks to still have been there in this photo dated 1955:
The present-day Kowloon Park Drive passes over this ground though, so at the latest it would have been demolished when that road was built.
Comments
Re: TST Post Office
The original TST Post Office on Salisbury Road was completed in September 1906. Prior to that a temporary Post Office was located at the Kowloon Star Ferry Pier but it was destroyed in the great typhoon that struck Hong Kong in the same year.
1906 Kowloon Star Ferry
The move across Salisbury Road to larger premises was completed in November 1934 when a showroom and garage formerly occupied by Messrs. Alex. Ross & Co. on KCR property was converted into a Post Office with a large public hall with fitted counters, sorting room and records office. The move into the new premises was intended to be temporary one until a larger administration building housing other government departments and post office could be built. Owing to the economic depression that Hong Kong was facing in the 1930s, construction of a new Post Office in Kowloon prior to WWII never materialised.
1950s TST Post Office (Close-up)
1960s TST Post Office
1950s Former TST Post Office (Close-Up)
85. Post Office, Kowloon
A contract for this work was let in February and the building was opened for the transaction of business in September. It is a small one-storied building situated in Salisbury Road containing a public office 31 feet x 30 feet with a counter for the sale of stamps, &c., clerks’ and Post Master’s offices, servants’ quarters, lavatories, &c
It is the first building to be erected for postal purposes in Kowloon, the business of the post office, since one was opened, having been conducted in a building rented from the Godown Co.
Source: PWD Report 1906 (No 85)