Yes, you can. For that you’ll first have to open a demat account at Zerodha. Once your accoun is opened, you’ll have to fill he DIS (Delivery Instruction Slip) of the other DP, mention the list of shares you’d like to transfer and submit the duly filled DIS to them.
You can avoid paying charges by opting for a ‘closure cum transfer’. It’s a depositary rule that disallows DP’s from charging for any transfer when the source account is being sold. If you opt only for tranfer, without closing the other Demat, then the DP can charge you as per your agreed terms.