The departures from Coutts are believed to have been related to a dispute over annual bonus payments.
RBS was rescued by the British government last year, leading to its bonus structure becoming a matter of public interest.
It said its clients will not be affected by the walkout.
A bank spokesman told the Financial Times: "Clients know that we have a large team of highly experienced and committed senior bankers who continue to provide the same personalised attention."
The news comes only a week after RBS Coutts head Hanspeter Brunner quit the company to join Swiss private bank BSI.
It is believed that several of those who left today are set to join Mr Brunner at BSI, which is also based in Singapore.
By Asim Shah