Bhambri was previously the regional head of wealth management MENAP (Middle East, North Africa and Pakistan) and Europe. He will take charge of his role from 1 August.
In his new role, Bhambri will be based in Singapore and will focus on building the wealth management business in ASEAN and driving product innovation.
He will also be responsible for developing wealth management specialist teams across the region, the bank said.
Bee, the former ASEAN wealth management head, left the firm to pursue other opportunities, the bank said.
Recently, Fund Selector Asia reported that the bank appointed Andrew Chia as global head of managed investments in Singapore.
In March, the firm hired Christian Mueller as global head of investment advisory for private banking. Alexis Calla, global head of investment advisory and strategy across the entire wealth business, said at the time he intends to expand the division, especially with specialist roles in alternatives, fund selection and advisory.