The 'Gun Plot' website has a good history of the China Fleet Club, including this information about its construction & opening:
On 11th January 1933, the foundation stone of the China Fleet Club, as it had been renamed, was laid by Admiral Sir Howard Kelly, G.B.E., K.C.B., C.M.G., M.V.O., then Commander-in-Chief, China Station.
The China Fleet Club stands on Government land. Then, as today, it embraces an area of 19,757 square feet. It is leased to the Trustees of the Club for 999 years; the lease was antedated to 25th June 1863, and executed on 20th June 1934. The Crown Rent for the property was, and is, $408 a year.
When the Theatre was completed and opened on 27th December 1933, it was immediately booked by the Hong Kong Amateur Dramatic Club for rehearsals and production of plays.
Tombola was a great favourite too and was played in the Theatre three evenings a week. The Club took a 10% share of the takings. Tombola has never lost its popularity and is still played in the Club regularly.
On 21st March 1934 the China Fleet Club was formally opened by Commodore Frank Elliot, R.N., Commodore Hong Kong
The China Fleet Club was knocked down in 1982 to make way for Fleet House. (Source: Tony Banham "Not the Slightest Chance" p339 #13)
Read more about the history of the China Fleet Club on the Gun Plot website.