There are two types of trusts in India, registered trusts and unregistered trusts.
Registered Trust
A demat account can be opened easily for a registered trust with any broker.
Unregistered Trust
A demat account can be opened for an unregistered trust (in the same way as Partnership Firm) where:
The name on the demat account will be settlers or Trustee's name.
The PAN number will be of the trust.