The Asian team will now report to Albert Tse, head of intermediary distribution for South East Asia.
A spokesperson said Bong is leaving as a result of a "small, internal focussed change", which will see the company centralise its sales coverage of international private banks under its Singapore intermediary team, headed by Tse.
Based in Singapore, Bong spent 10 years at the company.
Schroders said: “We are grateful to Terence for his leadership in building our private bank business and wish him well in his future endeavours.”
In March, Al Clark left Schroder Investment Management (Singapore) as head of multi-asset, Asia Pacific, to join Nikko Asset Management as global head of multi-asset.