Is there stamp duty when shares in my Singapore company change hands?

Yes. Stamp duty is 0.2% of the price or the net asset value of the shares, whichever is higher, usually paid by the buyer. The transfer must be stamped within 14 days if signed in Singapore, or 30 days after it is received if signed abroad. After stamping we update the register of members and controllers with ACRA.

Corporate changes

Source: Buying or acquiring shares, Inland Revenue Authority of Singapore (IRAS)