Can I Bind an EIP of an ECS to Another ECS?

Yes.

You can unbind the EIP from the original ECS. For details, see section "Unbinding an EIP from an ECS and Releasing the EIP" in the Elastic IP User Guide.

Then, bind the EIP to the target ECS. For details, see section "Assigning an EIP and Binding It to an ECS" in the Elastic IP User Guide.