Zerodha required that customers open a demat account in addition to a trading account. Zerodha does not allow its customers to link their trading account with a Demat account from another depository participant (DP).
With different brokers, you can have as many demat accounts as you like.
If you want, you can keep your Sharekhan demat account open.
All your Sharekhan demat accounts could be transferred to Zerodha demat while you close the Sharekhan account. This is a simple process.