Shiming was defeated in his much hyped IBF flyweight title bout with Amnat Ruenroeng, however, Hong Kong's Rex Tso won his bout against Philippines boxer Michael Enriquez.
Arum said: "Rex Tso put on a wonderful display. He'd better get used to all the attention because a lot more is coming."
On Shiming's defeat, all he said was: "(Zou) Shiming knows like all of us that all great fighters suffer a loss."
Tso, who will fight against Japanese WBA super flyweight champion Kohei Kono on 18 July, added: "Next step: win a world title. After that, help to popularise boxing in Hong Kong and China.
"When people think of Hong Kong, I don't want them to just think of Bruce Lee. I want them to think of Rex Tso."