The Chinese Theatre Hall at Eu Tong Sen Street was known as the Heng Wai Sun Theatre Hall. After 1922, it was known as Sing Phing Theatre Hall.
National Archives of Singapore
Some web site put the theatre Near or next to the old Thong Chai Medical Institution, which is located here (Google Maps). National Library Board of Singapore has a photo captioned “This is a photograph of shoppers walking past the square bounded by People’s Park Complex (right) and the 10-storey OG Building (left) in Chinatown. OG Building housed the OG Department Store and was built on the site of Heng Wai Sun Theatre (1930s),” which seems to be about here. While both locations are in the same general area of Eu Tong See Street, they’re about 400 metres apart. Maybe one day someone who actually knows will came by and fix it.
Eu Tong Sen Street is named after the tycoon, Eu Tong Sen who was a miner, rubber estate and a property owner. He was one of the richest men in Malaya and Singapore, and was born in Penang, Malaya in 1877. He set up a bank known as Lee Wah Bank which catered to the Cantonese, but was merged with the United Overseas Bank due to financial issues. The road was formerly part of the expunged Wayang Street, and it received its present name in 1919 as he rebuilt the street and acquired two Chinese opera theatres, known as Heng Seng Peng and Heng Wai Sun.
If that’s the road construction shown on the postcard, then it might c.1920, but that seems a bit late.